Hi wolfwolf
What kind of corys are you thinking about breeding? If it's C. aeneus (bronze or albino) or C. paleatus (Peppered corys), which are often the beginner's cory, they are easy to get to spawn if they are mature and well conditioned. Often a simple water change is enough to get them started. If it's some of the more unusual corys, they may take more effort. There are still quite a few species that have yet to be bred in captivity.
If you're pretty sure they're ready to spawn, and they don't do it on their own, try doing a good water change and bottom cleaning, and leave the heater off overnight. The water temperature will gradually drop, but not too much or too fast. Plug it back in the following day. Give them a week or so after that to see if they spawn.
If that doesn't work, try doing a water change and adding water cooler than what is in the tank, but don't drop the temperature more than about 5 degrees F. Again, wait and see if anything happens. If it doesn't, you will want to think about whether you want to continue and perhaps repeat the temperature drop every day for a few days. Unlike many tropical fish, corys don't usually get Ich, which is what you want to avoid by keeping the temperature stable, so it's best not to do this with a community tank.
If you're thinking about breeding corys, it's important to have patience. You cannot force them to spawn if they aren't ready.
As for "conditioning," since you live in the US, try to find a lfs that sells live blackworms. If you cannot find any, get some frozen bloodworms. They will make your corys strong and healthy and if they are mature, they'll help them develop a good number of eggs. Freeze dried brine shrimp is not a good food for this purpose. (To make it sink, try taking a few spoonfuls of tank water and adding it to some of the freeze dried product in a dish. Let it set until it absorbs water and softens. Then put into the tank.)
The ideal temperature for corys varies according to species.