Angelfish are extremely easy to breed. Purchase several angelfish; whatever strain(s) you like. The trickiest part is the watching part - for they WILL form a "pair bond" and you can easily notice this by watching closely. The 2 will swim together constantly. Once you have a pair, remove all the other angels from the tank. (You really have to let them do the choosing, thus the need for putting at least 6 angels together to begin with.)
Before long, you'll find them cleaning a site in the tank. Mine ALWAYS laid their eggs on the intake siphon tube for the filter, I'm guessing because there was a strong constant water flow. This was SOMEWHAT problematic, as the fry would no doubt get sucked into the siphon tube the second they hatched, so I turned that filter off when they were ready to hatch and relied on the second filter I had in the tank. Alternatively, I would take the siphon tube and put it in a floating baby tank for ease of feeding.
Once they hatch, remove the parents and feed the babies fry food - infusoria, algae water, daphnia, etc. It's easier to feed them if they are contained in a smaller space, such as a floating breeder tank. I also put several plants in the baby tank so that they could hide, rest, and pick at algae and other little bits.
Good luck, again, they're very easy if you just follow these steps. And unless you know what you'll do with all the babies, you might want to check with your local pet shops to see if they'll take some off your hands. Once angels are paired off, they almost always breed repeatedly, and you'll be over-run with angelfish.