Assuming you want to capture animals (groundhogs, horses, bears, dreaded Rhesus Macauqes) as opposed to vermin.
Build a cage trap where the animals roam (usually next to an outdoor food pile works well) with build, Traps, cage. You will need a mechanism and a cage. Mechanics skill is used to place the trap.
You should probably designate an animal stockpile (p, a) where the animal will be taken after it's caught.
After this, just wait for the animal to be caught.
Note: the capture live land animal option at the kennels catches vermin not animals.
Hint: placing your cage traps randomly can take too long to capture anything.
One way to increase the chances of an animal walking into your traps is to channel one long, 1-tile wide, dry moat(d,h) and remove all ramps(d,z) except one in the middle of the moat. Then you surround the single ramp with traps.
Once you've captured an animal, even if you're going to butcher it you probably want to get it trained at least a little, to avoid it breaking free on the way to the butcher shop. To train, make sure you have at least one dwarf with 'animal training' labor enabled, then find the animal in the status tab (z) and designate it for training. Butchering is also handled through the same status menu.
To train exotic animals you need a dungeon master. Once you have a Dungeon Master you can tame exotic animals. Once the animal is tame you can then train it as a beast of war.
In version .31 and upwards the dungeon master has been removed. He is no longer needed to train large animals in .34, in .31 he was. But there was a bug that prevented him from showing up.
Best Answer
Non-tame animals are bugged in 31.12 such that if they need to be moved more than a few steps, the dwarves carrying them panic, drop them, and flee, freeing the wild animal (or goblin) and causing chaos.
In addition to this, I believe the "slaughter an animal" task only applies to tame animals. "butcher a dead animal" is how you handle hunted animals, but this is hard given the abovementioned bug.
a) -- throw the animals into a pit. The pit must be as close to the cage with the animal as possible. once you have successfully "pitted" the animal, your marksdwarves / hunters can dispatch it at their leisure.
b) -- build the cage into a room, link it to a lever, station your military, and have someone pull the lever. Military will kill the animal, and then your butcher will run over and grab the corpse.