We keep and breed yabbies and marron, which are Australian crayfish, but the needs of all crayfish are the same (besides tank size, which is based on the size, and temperature to keep the tank at, which is based on where you're from.) However, I'd imagine you're from the states, and you're talking about the typical American Crawdad, or crayfish, which has nearly identical needs as our Aussie yabbies (I used to live in the states, my mum had some for a while for an experiment at her work...).
Crawdads are very easy to care for. They need fresh water, if you place them in salt water, they will die. A glass ten gallon tank would be ideal for a pair of fair-sized crayfish. You need a basic filter (under gravel, corner, whatever, it doesn't need to be as elaborate as you need with fish), and a tight fitting lid, as they can climb up any air line or whatever you have leading out of the tank, and escape otherwise.
For food, they'll eat basically anything. Really! In the wild they are scavengers, though if they can catch a fish, they'll eat it, they mainly eat carrion or plant matter, and detritous on the pond bottom. We feed ours once a week, just kitchen scraps; uncooked veggie scraps anywhere from carrot peels to pea pods to the ends of a cucumber, anything veggie, or slices of orange, apple, whatever. Give them this once a week, and once every month give them some lean red meat or calimari (squid, which we find works best). You can use the tablets you can sometimes find at petshops for them, too, sometimes you can find crayfish food, or use bottom feeder (fish) food, as well. IMPORTANT; do not overfeed them. Whatever you do feed them, don't leave it in the tank longer than two hours, or it will start to pollute the tank. If they eat it all, give them a little bit more, and remove the left overs after the two hours. Crayfish are hardy animals, but having polluted water, besides the chemicals that are caused by polluted water(Ie., ammonia, etc) are harmful to them, as they are to any underwater critter.
As for plants, you can put basically kind of plant in, but if you use real plants, the crayfish will eat them. Also, beware, they will dig practically anything you put in there up. They burrow by nature, and thus even if you put an ornament in the tank, don't be surprised if they've moved it quite a bit by the next morning.
For tankmates; we put top-swimming fish in without any problem (such as white-cloud minnows or guppies), but if the crayfish can reach them, they will eat them, so it does depend on how high the tank is, what the crayfish can climb on, etc.
If you want them to breed, this isn't hard, either. When you pick them up (do this behind the claws on the carapace (the main body the legs are attatched to, not the jointed tail), you're much less likely to get nipped then. Turn the crayfish over, and look at its legs. It will have five pairs, or ten legs in total (including the claws, the first set). If it's a mature male, there will be a small bump on the base at each of the fifth legs (the set closest to the tail), this is what the male uses it deposit his sperm on the female. If it's a mature female; the base of each of the third legs (the middle pair) will have a small oval or circle, this is where the males deposit their sperm.
They usually don't need any prompting to mate, two like-sized crayfish generally do it on their own, and the female will deposit the eggs onto the underside of her tail, and protect them until they hatch, and through all the separate larval stages the babies go through; until they start climbing all over her, and the tank.
It's recommended you remove both parents, then, and use the tank as a growout tank, feed them much the same as the parents, though supplement them with a few fish flakes every other day as they grow.