Birds have the great characteristics of being generally non-toxic, non-venomous, less prone to internal parasites, not likely to kill you (with the possible exception of cassowaries), and they taste pretty good. With some thinking outside the box, they are catchable too.
First the obvious - eggs don't fly away. Nest raiding is always an easy option, particularly for ground-nesting species. Eggs and chicks are easy prey. Many seabirds such as petrels and shearwaters nest in burrows. Their eggs are large, and their chicks are flightless and relatively defenseless until fledged. They can be caught by day by sticking your hand down burrows and waiting for them to clamp onto your finger, then just grip the beak and haul out. Two words of warning: a) The beaks and tongue have sharp serrations - use some protection; b) Snakes like both birds and burrows too. Depending on the species, some chicks may wander around by day. They are also likely to come out at night, so this may be preferable to sticking your hand in a hole. Additionally, petrels are pretty crappy at taking off from the ground so when they land you have a fair chance of chasing them down and grabbing them.
Throwing sticks and bola
OK, not too subtle or hi-tec. Throwing a stone at a bird is unlikely to land a meal because a) You have to hit the thing; b) You have to hit the thing hard enough to stun it. If you can approach a flock of waders or waterfowl eg. at a lake edge using reeds as cover, a (for want of better words) bloody big heavy stick flung at the group is more likely to hit and stun a bird than a well aimed pebble. To all you city-dwellers out there, any strike on an animal like this will be short-lived. You must follow it up quickly and not just wait for the thing to float to you wrapped in plastic with a bar code. Throw, hit, stun and immediately dash/swim and grab the thing. It doesn't need to be pretty, just grab it as best you can. Don't worry about hurting it, you will be wringing its neck in a second or two. As I said in my Disclaimer, I believe in being humane. A few rough seconds is preferable to a few minutes of the human being squeamish and prolonging suffering.
A bola is a very useful device to consider. The Innuit use it to catch seabirds, and Argentinian gauchos use it to bring down cattle. I'm surprised they aren't used more often. Wrap stones individually into pouches made from material, natural materials such as flax fibres, bark - whatever works as a small sack. If you have the cord and are so-inclined, monkey fist knots are ideal. These are in turn tied in about 90cm lengths together to a single point. The bola is used essentially by whirling it around to build speed, then flung at a group of birds on the ground (or at the legs of larger prey if they happen along - unlikely, but possible). It works in two ways. First, you have more chance of hitting a flock of birds with 6 stones flailing around, and second in the case of long-legged waders, they can get entangled. From experience, this has worked for me largely by just stunning and startling them. I've only got it around the legs a few times. If used where part of their escape is blocked by vegetation, they get a bit confused in their takeoff. I usually have to be pretty quick and chase them down with a big stick before they figure out what happened.
Netting, noosing, hooking
Entanglement methods are more likely to provide results. If you are fortunate enough to have a hank of monofilament net in your kit, then net spread along a gap between vegetation on a path or ridgeline will catch birds flying across the gap. This method works - it's used by zoologists to catch forest birds (mist netting). Mono net can also be placed strategically over and around known roosting spots for birds such as cormorants. Just as with fish (and soldiers!) entanglement generates a moderate amount of flailing and squawking. You are likely to get more than one bird if placed on colonial roosting spots.
In the absence of netting, a buttload of monofilament nooses on a stick (yes, I know I've recycled the squirrel noose image - I'll get a better picture soon) serves a similar purpose. Unlike the snares for trapping mammals, we are using a shotgun approach to entanglement. Place these along obvious funnelling points such as roosting branches (eg. cormorants) and paths through reeds on lakesides (waterfowl, rails bitterns).
A variant on the noose stick is an arrangement of nooses based on lure and entanglement. This is the principle used in the traditional Indian Bal Chatri bird trap . In traditional form, a cage containing live prey was covered in nooses with the aim of catching birds of prey. I have used a similar principle with rabbit entrails and carcasses as bait, minus the cage and just staking lots of nooses, to catch crows. The good thing about flocking birds like crows is that as soon as one gets into trouble, they all crowd and flap around so you are likely to catch more than one.
The entanglement principle can be enhanced by including (please see my Disclaimer before you send the hate mail) fishing hooks. Lines of fishing hooks tied along any path used by an animal will hold it long enough to be grabbed. This is one method I haven't used even in practice, but if fish (and fishers) get hooked by gang hooks, so too can larger animals.
Hooking can also be used on birds much as the same way as for fish - bait (offal, scraps), hooks embedded in the bait, and a stretch of monofilament line secured to an anchor point. Again, another method I haven't used even in practise, but one that is often seen by accident on any wharf with lots of recreational fishermen.
If you are fortunate enough to be stuck during the molting season for waterfowl (when they can't fly), then birds can be herded on the water into pre-prepared fence traps. This requires quite a bit of planning of the siting of the fencing, construction of the fence, and it is considerably easier with a couple of your mates to help. I have used this method often to catch waterfowl for banding. Admittedly from a kayak.
I remember as a kid trying to trap sparrows using a shoe box, a wooden clothes peg, and a piece of string - to no avail. There are a variety of traps in the literature such as a reef knot snare - when the bird lands on a loop, pull it. I really can't see it working. Another is the Ojibwa snare - according to FM 27-76 apparently used by American First Nations to snare birds with a counterweight and a perch array. These may work, but require quite a bit of engineering to get them right. I haven't tried it yet. Resin on branches to glue them down is apparently successful in some places. I'm less than convinced at its wide applicability. If anyone has any methods that work - with evidence, mind! Let me know.
Preparation and cooking
Birds are easy to prepare. If you intend to collect the blood - advisable as it is rich in iron - be careful to cut the jugular and/or carotid arteries in the neck, but don't cut the oesophagus. Basically - cut the veins and not the big tubes. Collect the blood. If you do cut the oesophagus, then stomach acids will drip into the blood. Once bled, cut the head off and slice the bird up the belly and scoop out the insides. Keep any eggs, the liver, heart, and kidneys. These are generally relatively free of parasites and are nutritious.
The bird can then be easily skinned for boiling, or plucked and roasted over a fire. Actually, it's not even necessary to pluck if you are simply throwing the carcass on embers, but it reduces the smell a bit. It is preferable to dissect the bird into pieces to ensure even cooking. From a health perspective, boiling is a more reliable way of killing pathogens. Basically just put the meat, kidney/liver/heart, cracked eggs, & blood into a big stew. If roasting, spread the carcass on a rack of sticks to ensure it is cooked well through.