They're pretty much like any other cory as far as breeding triggers go. I do find, though that they don't produce clutches as large as say the bronze cories (up to 200 eggs at once?! My pandas have never done that!). Mine mate several times a week, but only produce about a dozen or so eggs each time.
Provide plants for them to lay the eggs on, and feed a varied diet (mine get flakes, algae wafers, bloodworms, and zucchini). Keep the water quality good; I do 50% water change with vacuuming (in the unplanted areas only, as the Crypt areas are too dense to vacuum in) weekly. I frequently see mating activity immediately after water changes.
If I want to raise up some fry, I have to take the eggs out of the main tank, otherwise the tetras eat them and the wigglers. If you have a dedicated panda tank, a good clump of java moss, other bushy plants, or sticks will provide likely be enough protection for the fry and you can leave them in with the adults (no personal experience with this, though, so take that with a grain of salt).
Fry care is like other cories- clean water, plenty of fine-particle food, mid 70s temperature, and lots of water changes to get out the uneaten food. The eggs hatch in ~5-7 days, and start eating about three days after hatching. It takes 7-8 weeks after hatching for the fry to fully color up and look like a miniature adult (~3/4 inch long).
They're great fish, and tremendous fun to raise. I have a series of blog posts about the first few batches of eggs I raised, if you're interested in looking. Here's the
direct link to all the panda cory posts, so you don't have to wade through all the knitting and weaving and other non-fishy posts.