Alright, here's some info to digest.
Domestic bred angelfish often eat their fry, as they are raised more often for their color and finnage rather than their parenting abilities. However, you can still easily raise them in a hatchery tank if you like. Just make sure to brew some fresh baby brine shrimp, every day for at least the first 2 weeks. Feed them fresh BBS for the first 6 weeks before slowly weaning them to flake over the next 6 weeks. By the time they hit 12 weeks, they should be about dime to nickel sized if you keep up on your water changes and feeding schedule.
A great hatchery can be made from a 10g tank, small powerfilter (AC Mini), prefilter sponge for powerfilter intake tube(Tetra Brilliant), and a 50w heater. Your best efforts will be made by having a barebottom hatchery (no substrate), as the fry tend to commit suicide in gravel, and sand will develop bacteria that can cause issues with development of the swimbladder and bloat.
Often I will add 1 drop per gallon of each Methylene Blue and Malachite Green, just a minute or so (allow time for it to mix in) before pulling the eggs from the parent tank and rubbing them very gently off the spawning slate/pvc tube/leaf into the hatchery. Don't go too overkill on the Methylene and Malachite, as Malachite can harden the outside of the eggs to the point that the wrigglers have a hard time hatching. Also, make sure the flow of the filter is slow so that eggs aren't being tossed too much. Also, a teaspoon or two of salt is good to help prevent bacterial bloat once the wrigglers have hatched.
Your eggs should be translucent or slightly white in color, which means they are fertile. However, if they are solid white, or showing any signs of fuzziness, those are fungused eggs which haven't made it. Also, you don't have to be too terribly concerned about exposure to air for a few seconds between the move of the eggs, and just make sure your hands are clean but not soaped when rubbing off the eggs. Tempature being similar is good enough with eggs.
Basically, once you've moved the eggs, you have about a 5 day wait until they hatch into wrigglers. After about another 48 hours they should start freeswimming. If you've made it that far, Congratulations!
After that, it's time for growout as you get to watch the little buggers develop dorsal and anal fins, then ventral fins.
Don't forget to cull any baby angelfish that have deformities of any kind, or ones that aren't showing good finnage and color. It may sound cruel, but so is the way of nature.
Hope I didn't skip around too terribly much, just woke up and still a little scatterbrained.
Good Luck,
Raithan O. Ellis