I will try to find the article I followed again, but here is the jist of it.
2 males to 1 female is a good ratio.
Feed them very well, or overfeed (like you can overfeed with those little hoovers)
Do a good water change, and put in slightly cooler water. This mimics their natural habitat, where an influx of fresh rainwater during the rainy season signals them to start breeding.
The female will like to lay her eggs in a spot with good water flow. Mine like the pennywort under the filter outflow. The moving water helps keep the eggs from getting gunky. Some people also put shrimp in the tank to keep the eggs clean.
The cories will eat their own eggs. So either put them in a hatching tank and remove them when they are done, or give the eggs a couple hours to harden up and then you can move them (I use a soft toothbrush).
The eggs should be in water just like what is in the breeding tank. So, the easiest way to raise the eggs is to put them in a breeder box in the tank so the other fish cant eat them. I have a net breeder that I hang inside the tank so it gets water flow through it, and put some java moss in it.
The eggs take about a week to hatch. From what I can see, the fry are free-swimming within a day, but still stay on the bottom. Mine do fine on just flake food and detritus. I've never had to feed them a special diet.
If you follow the link in my sig you can see all my sterbai babies.