Direction finding without a compass
Sometimes we may find our compass, our spare compass, and our Satnav all got eaten by the same dog, along with our homework. Or, for convenience's sake we don't want to whip out or compass every 3 minutes. All is not lost.
Using the sun to determine direction
There are two quick-and-dirty methods to determining direction using the sun.
Use your analogue watch to determine direction from the sun
For those smarty-pants out there with nought but a digital watch or, even worse, only a smartphone you will have to use some imagination. The exact method depends on the hemisphere you just happen to be in. In the northern hemisphere, hold the watch horizontal and point the hour hand at the sun. Bisect the angle between the hour hand (the dark one in this illustration) and the 12 o'clock mark to point to SOUTH. For some inexplicable reason the illustration I borrowed from US Army FM 21-76 makes a special point of the stick. You do not need a stick. I think the illustrator just put it there for decoration. Kidding aside, I think they put the stick there as an aiming point to help you align the hour hand to the sun - it's preferable to align three points further apart, rather than just the center of the watch, the hour marker, and the sun. They just didn't mention that in the manual.
In the southern hemisphere point the 12 o'clock mark at the sun. The bisected angle between the 12 o'clock mark and the hour hand will point to NORTH.
If you find yourself a bit challenged as to which points North vs South - if you're in the Northern hemisphere, the Sun is in the southern end of the sky (toward the Equator); and in the Southern hemisphere the Sun is in the Northern end of the sky.
Regardless of hemisphere, these methods assume local time - not daylight time. They are also more useful in temperate zones. In the tropics they are of limited use. A better method is the following...
Stick tip shadow method
Set a 1m long or so stick in the ground - the good old US Army FM 21-76 specifies
it must be straight. The straightness is largely irrelevant, but there you go. Mark the shadow of the tip of your stick with an object - a stone, a mark in the dirt, whatever. Wait about 15 minutes - longer if you can - until the shadow position has changed enough to be obvious and mark the second tip of the shadow. Draw a line between the two shadow tips - this is the East-West line. Which is which? I hear you ask... The Sun rises in the East and sets in the West, so the first shadow mark is West, the second one is East. Why the reversal? you casually ask, knowing the answer already. If the sun is in the East, the shadow will be cast to the West, and vice versa - of course, silly-billy! Put your left foot on the first (West) shadow mark, and your right foot on the second (East) shadow mark, and you are facing North. Too easy. There is no hemispheric conversion required for this one - it's irrelevant. The Earth rotates in only one direction. The position of the stick - whether straight or slightly wonky - is irrelevant. It will be in front of you in the South hemisphere, behind you in the North hemisphere. Just don't sit on or trip over it.
Night-time direction finding
The moon can be used as a very broad East-West indicator. Remember moonlight is the reflection of the sun. So with a bit of mental gymnastics, if the moon is up before the sun has set, then the light side of the moon must be to the West - the same side as the sun is disappearing/has just disappeared. If the moon rises after midnight, the reverse is true. The light side of the moon is on the side the moon is about to appear to - it rises in the East. This is a rough and ready way of at least not confusing North and South.
Using the stars to find North in the Northern hemisphere
We northern-hemisphere natives are lucky in that there is a star that pretty much hovers over the North Pole. Well, technically the Earth rotates on an axis that conveniently has a star that just happens to be near the axle of rotation. Rather unsurprisingly, this is called Polaris or the North Star. A word of caution - contrary to some common opinion, it's not the brightest star. Capella, Arcturus, and Vega (and probably some others) are brighter. Not to mention some annoying planets. To find the star we need to know two constellations - Ursa Major, referred to as the Big Dipper or the Plough - although these are only a part of the constellation; and Cassiopeia - the W.
Now bear with me here... Polaris is the end of the Little Dipper handle (the bit you would hang on a kitchen hook). The Big Dipper and Cassiopeia are used in combination to point to Polaris. The Big Dipper and Cassiopeia are always opposite each other, and of course rotating (from our point of view) around north. As are all the other constellations in the hemisphere. The Big Dipper has a seven star group in its characteristic shape. The two stars forming the outer lip of this dipper are the "pointers" because they point to the North Star. Mentally draw a line from the outer bottom star to the outer top star of the Big Dipper's bucket. Extend this line about five times the distance between the pointer stars. The North Star lies along this line. I've drawn some arrows here to show the basic principle.
This brings us to Cassiopeia, which has five stars shaped like a "W" on its side. The North Star is kind of straight out from Cassiopeia's center star. The intersection of these two arrows indicates Polaris,and clears up any confusion about which is the Big vs Little Dippers. An imaginary line dropped to the earth from the star indicates North.
We northern-hemisphere natives are even more fortunate in that Ursa Major and Cassiopeia (and of course Ursa Minor) don't set in the Northern hemisphere. Those redneck inbreds in the Southern hemisphere have to deal with a constellation that keeps on setting. Another argument why brother and sister should not wed...
One confusion that could arise, following a question from one of my many, many, friends is that it is conceivable that the Little Dipper and Cassiopeia could be confused with each other because Cassiopeia, with a bit of imagination, does indeed resemble a Dipper of some kind. You just need to practise and eyeball them. Cassiopeia is brighter. And yes, any group of stars can be visualised to look like any shape. I told you those greek astronomers were on drugs...
Using the stars to find South in the Southern hemisphere
We southern-hemisphere natives are lucky in that, despite we don't have a star that hangs around the South Pole, to find a cardinal point we have a far easier set of stars to use - the Southern Cross. Yes, it points to South, not North - but that's to be expected given we're on the southern end of the rotation axis. The Crux or Southern Cross (technically the Crux consists of more stars than the Cross per se) has 5 stars - think Australian flag, unless you're a New Zealander in which case one of them seems to have disappeared. To find south, extend the long axis of the cross 5 times its length, drop an imaginary line to the Earth, and this is South.
Our estimate can be improved by, as in the northern hemisphere, looking at the intersection of another set of stars. On the opposite side of the 5th star in the cross are a pair of very obvious stars - Alpha Centauri (Rigil Kentaurus) and Beta Centauri (Hadar) - of course... These are the Southern Pointers. An imaginary perpendicular bisected line drawn from these stars to the projected 5x the axis line of the cross narrows down the estimate of where south is (well, is close enough to). There are two problems with using the Southern Cross. There is another similar-looking arrangement - the 'false cross'. The false cross is actually a group of stars borrowed from two constellations - Vela (the Sail) and Carina (the keel). Together these form part of a big ship, apparently. I swear those ancient Greek astronomers must have been on some heinous drugs!
The false cross is fainter, and there are no pointer stars close by. On the bright side, with changes in the Earths rotation axis it will indicate South in about 6800 years time, when the pole has gradually shifted to a point just east to the intersection of the False Cross cross-arms. I digress. The Crux and false cross are hard to confuse once you've seen the real thing. The second problem is that the Crux and the pointers will set - they may not be around at some times of the night or indeed year - depending on latitude. Below 34 degrees South it is visible year-round. Above that it may be very low on the horizon and dip below it.
There's always going to be some smart alec who asks If you're so clever, Mr Eazy, what if I'm at the equator? Upon which I will slap them unceremoniously upside the head. Here's the upshot - the Southern Cross will be visible at the Equator From February to June. So for all of you Southern Hemisphere sheep-worriers, you'll have to do a crash course on Polaris to deal with the rest of the year.
Polaris is visible year-round at the Equator, but finding it is a different matter. As I labored above - we can use Cassiopeia and/or the Pointers on Ursus Major to point to Polaris. It just so happens that Cassiopeia is in the Equatorial sky from February to June, and Ursus Major is in the sky from July to December - remember the two are opposite to each other from Polaris. Between the two you will be able to figure out which is Polaris. As an aside, Cassiopeia and Crux are on opposite sides of the Earth - they can never be seen together (from the Earth). To all you Flat-Earthers out there - In your face!
Aids to predicting where stars are
A useful tool to predicting astronomic data is either a hard copy star almanac or - bless the internet - locate a program that will show you the night sky at any given position and time of day/night. I use Stellarium. It's free and it plays nicely with Linux. If you plan on setting out, check where in the sky the appropriate constellations will be and at which time, note it in your notebook, and make it easier for yourself. This will be of particular importance in tropical latitudes, or in the Southern hemisphere above 34 degrees, when the Southern Cross will be a bit iffy.
Stellarium screen grab