If I had to sum it up in one phrase - Flick your bic! Disposable lighters are great, although Richard Graves bemoaned the fact one of his took 6 strikes to light. But admittedly it had been underwater for a day. Personally, I have never had any great need for making fire, but that's the 'army' in me. Unless I'm using it to blow something up, it's of little use. However in survival situations it serves for both morale and the 'real' necessity of keeping you warm. Let's look at ignition systems first.
Civilized humanity's magic
Keep a stash of disposable lighters secreted about the place. They ignite even after being wet (with a bit of drying), and are easy to use. Some of the 'safety-nazi' makes have childproof steel bands on them. Rip these off with a pair of pliers before taking them out. When you can't move your fingers, because you're cold and you can't light your lighter - well, it's annoying. Unless you have a convenient 5 year old child handy who can light it for you. As an aside, don't throw away spent lighters. Cannibalise them for the flints - the artificial flint when scraped sharply against steel will generate sparks.
I strongly recommend carrying a firelighting flint of some kind. They are generally cheap and light. Two common types are a flint and steel scraper, like the one pictured. An alternative (and in my mind preferable) type use magnesium shavings. Magnesium reacts very quickly with oxygen, so is stable under most conditions as it basically rusts instantly. However, freshly shaved magnesium reacts very quickly with oxygen and a spark and burns at a few thousand degrees. Great stuff. I carry one (not the one pictured). Check out product reviews and have a play with different types if you can. Some brands are a bit flimsier than others. And, as with everything - practice!
Field expedient methods
Magnifying glass on tinder
We've all done this in one way or another, admit it. As a kid I used magnifying glasses to set fire to paper. I also burnt my hand unintentionally with a wine glass (when I was a bit older). I guess I wasn't paying attention, and my hand was at the focus point. Sunlight concentrated onto tinder can ignite it.
Wait a minute Eazy! I hear you say. I'm in the middle of bloody nowhere, where the hell do I get a magnifying glass? Take a close look at the baseplate of your compass. Bingo. If you have two compasses, you can concentrate the heat even further. If, like me, you carry binoculars then you are set. If you are closer to civilization, dirty filthy humans being what they are tend to throw out things like glass bottles. Hey presto, a concave piece of glass.
Various survival books have a range of variants of rubbing sticks together to make fire. The most reliable method I've used is the fire bow. The reason is simple - you can generate more friction for longer with the mechanical advantage of a bow. To construct one, you need an object to serve as a spindle for the drill. This is usually described in the manuals as 'hardwood' but in reality it could be a stone, a heavy shell - it's only there for you to hold so you don't drill a hole in your hand. If you can, lubricate it somehow with soap, candle wax or similar (I've seen ear wax suggested by some. Yum!). If it is wood, carve a wee depression for the blunt end of the drill to fit into. Typically, I try to find a convenient stone with a suitable depression. Second is the drill itself. This MUST be a dry, reasonably straight and robust stick, whittled to a point at the business end. If you can get a hardwood,that is good. Softwood generally works as well, but it must be dry and physically hard. The basepiece is a flattish piece of softwood with a shallow hole carved out about 1cm from the edge. It needs to be big enough for you to place your knee on it to hold it in place. Cut a V-shaped notch about 5mm into the edge of the hole. This collects the (hopefully) glowing embers. The bow is typically about 60cm long. This can be green wood - reasonably sturdy but flexible. If you can find a convenient forking branch in a tree like in the diagram, these make ideal bows. They are already kind of in the right shape, and the wood fibres are usually flexed to be stronger along the outside of the fork. Make a notch at each end so the string doesn't slip, and tie and tension the string. You will have to experiment a bit with tension. Use paracord or a bootlace. Flat bootlaces (cf round) are pretty good.
Now for the bit the books don't tell you (They tend to say 'Use the bow until you make fire...')
The hard work. Wrap the drill in the thong so the wrap is on the outside of the drill as pictured. It tends to ride over itself otherwise. Kneel on the basepiece to secure it, seat the drill into the hole, and get your body weight above the axis of the drill as much as possible. Doing it at arms length is a waste of time, you need the weight to increase the friction. I brace my hand on my knee, and try and get as much shoulder pressure as possible over the spindle.
Now for what I call conditioning the setup. Give it a bit of a workout to see how the system is working. You may need to change position a bit, tension the cord - basically just get a feel for it. Get into a rhythm of working the bow - you will need to keep momentum and pressure for a while. If the bottom of the hole is getting warm, you are on the right track. Often it helps if you have some abrasive materials in it such as coarse sand granules - not too much, just enough to increase friction. If it is starting to smoke, you have crossed the first hurdle. If you are at the smoking stage, you will see brown dust being generated at the bottom of the hole. This (and I love this name!) is called punk. As an aside I first encountered this word in print in Mark Twain's Tom Sawyer. Tom and Huck referred to 'punk stumps'. I had no idea what they were at the time. Hey, I was only 7. It's the 'Merican term for the rotting dry inside of dead logs.
If you have the right wood the punk (snigger!) should be slightly gritty and warm. Basically it is approaching charcoal, which is good as tinder. What can I say, punk rocks! Sorry, couldn't resist. Now you put loose fibrous tinder into the V-notch. Have a decent amount available, place it into the notch, but don't pack it too tightly or there will be no oxygen for the fire. Back to the punk production, put your shoulder into it and give it about 30 fast strokes, lift the drill and slide some tinder into the V-notch while blowing gently onto it. What we are trying to do is slide tinder into the hot spot where eventually it will light. Back to the bow, and repeat as necessary. As more punk gets generated, it acts like its own tinder and abrasive in one. Keep sliding tinder to make sure it is in contact with the punk, and blow.
When smoke starts to rise, fold tinder over the hole and basepiece. Ensure there is contact with tinder and the glowing punk, but don't kill it with too much. Blow... If necessary, back to the bow for 20 or so, then blow. If there's smoke, there is fire. You just need to get enough contact with the spark for the tinder to catch alight.
This method works! There is some need for experimentation with materials and technique, but once you get the hang of it things are sweet. Needless to say, once you get a good bow set together - hold onto it. Finding good materials has in my experience always been the stumbling block. Not every forest in the world has both hardwood and softwood, and the times you need fire the most is often in the places where dry wood is least abundant.
Now while there are a lot of chemical combinations that can be used to make fire, only one is likely to be available in a typical survival situation. Potassium permanganate (KMnO4, permanganate of potash, Condy's crystals) should be included in your first aid kit as an antiseptic and emergency water purifier. When ground then mixed with ground ordinary sugar (don't grind them together, campers, until you want to make flame!), the combination is heat sensitive and can be ignited with friction. Grinding between rock and a knife blade works, as does piling a bit in your fire bow notch and hole. I've seen different published ratios of KMnO4:Sugar - Wiseman cites it as 9:1, Graves as 2:1, the WA police Survival guide as 1:1. It's closer to somewhere between 9:1 and 3:1. Hey, what can I say, I like (indeed, I'm kind of trained to) blowing things up. Oh, and basic high school chemistry. The KMnO4 is the oxidizing agent (the important stuff) working on the energy-rich substrate (sugar), so you need more of it. Experiment before you need it - it's not a totally exact ratio. Moisture in either of the crystals will also alter its effectiveness. In addition, some manufacturers may put other chemicals that may act as flame retardents into it - so find a brand you like. Also be aware the reaction is pretty fast - just a pretty flash if you only have a small amount. I generally make a lot (ie. a tablespoon - I'm not crazy!) of the stuff and have a fuse arrangement to a larger pile in the middle of very fine and dry tinder. If you don't have a lot of the stuff you won't get enough heat. There are better field-expedient incendiary first-fire mixes that you can fabricate, but the typical hiker is unlikely to carry the materials.
As an additional note on field-expedient chemical methods. There is a lot of dodgy 'advice' out there. I've seen folks swear that adding a few drops of water to the mix generates the reaction. Anyone heard of high school chemistry? At least it's not dangerous. You just end up with purple sugar water. Admittedly when it dries out, it forms a pre-mixed friction-sensitive material. Not the sort of thing you want kicking around in your pack. Just like detonators and explosives, don't mix them until you need it. Glycerine one the other hand will spark it, but who carries glycerine around with them? Do some proper research (and a bit of small-scale experimenting before you need it). For my money, just secrete a few more bic lighters in nooks of your stuff.
For all you hunters out there, you have an ignition source with you. Gunpowder needs only a spark to light. To do this, of course, you need to carefully remove the pointy end from the round. I've done it with two pairs of pliers, but I only typically carry one when civilian hiking. Some sources suggest wedging the bullet into the barrel, and levering it loose from the case. I've never tried it - if anyone out there has dared, let me know. I certainly would not recommend doing it with a rimfire cartridge. The published wisdom is then either to pour the gunpowder out and ignite it as a first fire from a spark, or pour out half the powder, and wad the cartridge with cloth material as a flammable wadding, fire it into the air, retrieve and add the burning cloth to the remaining powder. It does work after a few trials of trying to find the wad of material you've just fired into the ether, but applying pliers to .30-06 cartridges with reckless abandon, or shoving the round head-first down your rifle and jiggling it takes a bit of nerve.
Tinder is critical. You can burn as many matches as you want, but you still won't set a log alight. You need to start small. But first, in your basic kit you should have a stash of solid fuel (hexamine), and in your emergency kit a candle. Hexamine and candles are easy to light. If available, light these to get the main fire going. Needless to say, if you are in a survival situation your hexi is precious. Only use it for firelighting, don't use it for heating or cooking.
Natural tinder sources basically consist of anything dry and fine or fibrous. Match-thickness dead twigs picked directly from the bush are always good. Anything on the ground will usually be too damp. Stringy dried leaves, dead grasses, dead fern fronds, seed husks, dried animal dung, lint from your socks - anything dry with a large surface area is good. Don't skimp on tinder. Collect lots, and when lighting a fire from the flame, use a big handful of the stuff. If you are using matches, they will be in limited supply so make the most of them. If you are using DEET insect repellent (the strong stuff), rubbing DEET on the tinder will help give it a head start. Imagine what it's doing to your skin? In the army I used to use it on my neck to warm myself on piquet duty.
What can I say? Dry, with sizes ranging from your tinder, through to finger and maybe arm width size. Split them if you can to increase surface area. Set yourself up for as long as you need the fire - don't run out in the middle of the night. If your larger pieces are damp, stack them around the fire to dry. Doing this will also reflect the heat back at you. Try to keep your fires as small as you need.
First, clear your fire area of leaf litter and other flammable material - ideally a 1m radius. Errant sparks can very quickly spark grassfire, particularly in very dry places such as (pretty much most of!) Australia. In addition to ignition and fuel, fire needs oxygen to burn. This is where most fire-making attempts fizzle out. Man, I crack myself up! There are lots of potential setups, the US FM illustrates the following:
Tepee style. Tinder is stacked in the middle and when ignited the smaller sticks are dried and ignited, falling into the center. Generally a good arrangement.
Lean-to style. This is a good arrangement when you have a directional wind. Shove a reasonably sturdy green stick at about 30 degrees from the ground, facing into the wind, and stack the larger (and possibly damper) larger pieces downwind. Its disadvantage is that the embers aren't concentrated in one place - you have to rake them around.
Cross-ditch. This is not so much of a wood-stacking arrangement as much as a way of getting oxygen to the fire. If the wind is coming from various directions, or indeed completely still, digging air trenches to try and channel air to the base of the fire can help. If the wind direction is obvious, then you don't really need the cross arrangement. Just align the trench parallel with the wind direction.
Pyramid. The pyramid can be good, depending on how you set it up. I've seen folks set them up with a small kindling fire in the centre - this basically just fizzles. Good old FM 21-76 in their description of this set up state the kindling fire should be set on the top and allowed to burn through. I'm not fully convinced that will always work. I use Graves' approach of having the pyramid stacked closely around a teepee (or conical) fire. You get wind protection, wood drying, and the smaller wood at the top will ignite and fall to the center to build up the ember base.
Final notes... When building a fire on a wet base such as sodden ground build it on top of a wood base. If building on snow, try to excavate to ground level, with a wide circle. I would probably put a base under it as well to deal with any melt water issues. If building a fire on snow under a tree - beware of snow falling from the branches above. It can be a real bummer.