First off, congratulations on the eggs! What type of cories do you have?
Some people may do this differently, but this is how I do it. They will eat the yolk sack for the first 24 hours then I usually start mine off on microworms. You can get a culture ready to feed the fry off of aquabid (I have used the seller Sonic before with success). You can feed the fry the microworms for a couple of days or so. You can also feed them baby brine shrimp. Once they are big enough, then you can start feeding them crushed flake and tablets.
The last set of fry I have raised, I didnt have any microworms. I fed them frozen BBS and it worked very well. I also have been feeding them Boyd's Vita Diet, which is a very small crumble full of nutrients. Its small enough for them the eat. They are now about 2 months old and are eating full size flakeds and frozen blood worms. They have grown a lot faster and bigger this time around.
Good Luck