Depends on the fish, but in general:
1) Ample space. Oh, heck, make that quite a good amount of space. Fish won't *talks in voice of Nappa from Dragonball Z Abridged* BREED FOR YOU *Voice back to regular* in cramped up places.
2) Good food. A varied, nutritious diet needs to be offered. The food should be of good quality, so always take the Hikari over the brand X.
3) Temperature. Not much of a concern where I live since most of what I'd want to breed are tropical and I live in the Philippines, but that aside, keeping the temp at a comofortable range would be a start. Alternatively, research on the specs of the species you'll be attempting to breed, as some species are most likely to breed after some small changes in temp (Mimics rainy season).
4) Aquarium setup. Each species has different breeding behaviours and methods and depending on what you get, that will help you decide on the design for you're breeding tank.
5) NO TANKMATES. Self-explanatory.
6) Extra aquarium. For the parents/babies. Especially if parents will eat babies.