http://www.ee.pdx.edu/~davidr/discus/articles/artemia.html has a great deal of info on the species itself.
Shrimp are more work but are more fun. I've found brine shrimp to be rather easy if your only intention is as a food item for other fish. They basically just need salt water and air. Eggs are readily available and store bought eggs have a fairly high hatch rate. You can also buy them in ready to use mixes that contains the salt and ph adjusting chemicals mixed with the eggs that just need added to relatively warm water, around 80 F.
PetSmart and other retailers sale a variety of eggs and hatcheries but you can build a basic hatchery with some two liter soda bottles, a simple light and and a cheap air pump.
I recommend "San Francisco Bay Brand Shrimpery" if you only want feed for fry or treats for your adult fish. It uses a neat little trick to make the newly hatched shrimp congregate in a seperate chamber and at < 10$ is far easier than buiding one. It also works well as a quick way to hatch eggs and seperate the live shrimp. You just need to remove them quickly to a dedicated shrimp tank (or to your fish tank to be lunch) or they will die within a couple of hours of moving to the light and freshwater. The shrimpery makes it really easy to get started and it's far easier than building one.
Once hatched, a simple salt aquarium is all that's really necessary to raise them if you want larger sizes. For < 30$ I was able to get a hatchery, 1 gallon tank, salt, eggs and fine mesh net at the local lfs. Food takes the form of yeast. Brine shrimp will eat anything they can swallow which borders on microscopic. Add a 1 gallon basic aquarium kit (the kind with a under gravel filter & airstone included) and you have all you need. A tube of eggs probably has thousands in it. The under gravel filter also makes cleaning cysts (egg shells) easy to clean. Once they reach the desired size, add them to the tank with the hungry fish. Dump the shrimp tank, rinse and begin again. I don't let them get near maturity so the smaller fish can eat them but if you want larger brine, you will need a bigger tank. They molt frequently and will quickly polute the water.
You can build cheaper but I haven't seen where saving a few bucks is worth the trouble.