What sort of cory eggs are they? Cory's are really easy once you've done it a couple of times. I've got hundreds of bronze corys because I can't stop them breeding!
I have a small tank (20l) with water from the parents tank, a sponge filter and an airstone, at about 28*. I take the eggs out and put them in the small tank. Do it within 24 hrs of the eggs being laid, or they harden and aren't so sticky. Scrape them off with a clean credit card or something like that, and stick them to the sides of the small tank. Don't worry about the ones that don't stick, they hatch too.
You can either have the tank in a dark place, or use meth blue. I used to use meth blue, but now just leave them in a dark place which prevents the eggs from fungasing. At 28*, they take about 72hrs (3days) to hatch. The lower the temp, the longer they take to hatch.
You can tell they're hatching because some of the eggs start to look like there's just a piece of shell there where the egg used to be. The babies are tiny, and just roll on the bottom for a few days. When their yolk sac has been used up, you can start feeding BBS (newly hatched), decaps BS eggs, microworms etc. Generally you can tell that their yolk sac has been used up when they start swimming around a little bit. I start feeding in about 2 days. Little and often is the key.
Some babies will die, but don't be disheartened - this is just what happens. For the first 2 weeks, do a 30% w/c every day (not much in a 20l tank), use airline to syphon the dead babies and eggs that haven't hatched. I use room temp aged water for the first few days, but I've also used straight tap water and they've been fine. You could use water from the parents tank also.
After about 1 1/2 weeks, the start looking like mini corys - they have tails and fins and everything. When they start getting the colour of the parents, it's a good idea to move them into a bigger tank or split them so they have more space to grow, this way they'll grow much faster.
From about 3 weeks, they can start eating real food - algae flakes, veges, flakes, the odd shrimp pellet. These guys are really really easy to hatch and grow out, so next time you have a spawn, I urge you to give it a go - you'll have hundreds of babies in no time!
If you've got any questions, let me know and I'll do my best to answer.