How does one make an Animal mob spawner?

I would like to know what necessary steps must be taken to successfully complete a spawner that spawns non-aggressive mobs such as, cows, chickens, sheep, and swine.

Edit: Although passive mobs can still spawn on Grass blocks at a light level at 9 or above, changes have been made to the spawn system since this answer was written. Previously, passive mobs would spawn and despawn similarly to hostile mobs, and this was an efficient way of gathering drops from passive mobs. However, with the addition of breeding into the game, making farms and breeding animals allows you to have a constant supply of items.

If you wanted to construct a building that farms passive mobs, you could make one similar to an aggressive mob farmer, but instead of a pitch-black room, you would cover it in grass and make sure the light level is above or equal to 9.

Since this is really all there is to it, these are the grass-growing behaviour:

A dirt block must be placed with no solid block or fluid on top of it and have a light level of at least 4 to accept grass. Grass can spread to any of the immediately adjacent blocks in the same layer, including diagonally. Grass can also spread to blocks one level above or three levels below the source block, even if the grass/dirt blocks are hovering in the air with nothing else directly touching them. - Minecraft Wiki

Additionally, torches give off a light level of 14, so you could place torches in a grid pattern with 4 in between each, ensuring that every block would have a light level of at least 9 (not the most efficient, but easily tillable):

TT 13 12 12 13 TT | TT = Torch
13 12 11 11 12 13 | ## = Light Level
12 11 10 10 11 12 |
11 10 09 09 10 11 |
11 10 09 09 10 11 |
12 11 10 10 11 12 |
13 12 11 11 12 13 | 
TT 13 12 12 13 TT |

Assuming you're talking about the monster spawner block, there's currently no way to do this from ingame without either /give or inventory editing.

Once, however, you do have a monster spawner in your inventory, all you have to do is place it in a lit area (light level 9+). It will then spawn pigs, and pigs only, unless you change it with a spawn egg.

If you need spawning for an adventure map, look into spawn eggs. Put them in a dispenser, hook it up to a pressure plate and a restone clock, then wait. Hilarity ensues.

If you're talking, in general, of a structure that enhances spawning, I'm not aware of ways to do so. You can easily attract nearby mob (friendly and not) in a small lit dip right outside the area you usually wander through and ensure that they spawn all the time through sufficient lightning; you can also easily trap the mob inside the dip (a two meters dip is enough).

Remember to check the dip frequently, for mob (friendly or not) have a lifetime of ~12 ingame hours (personal experience).