I haven't found that bettas are hard to keep (at least, no more difficult than other tropical fish). They're pretty hardy (they're the ones you sometimes see sold in vases and things- admittedly they're very hard to keep alive in a vase!)
You'd need a tank, a heater, and a filter for starters. General fish-keeping website will give you more information. You can get betta-food, or
feed live or frozen foods (I use a mix of a flake food specifically for bettas, and frozen food- all purchased).
You can't keep bettas together, but you can get tank dividers to turn a big tank into several smaller ones to keep multiple bettas. Bettas are carnivorous, but there are some other fish they can be kept with (I've kept Bettas in with some neon tetras without problems). Don't put them with anything nippy- they'll chomp on the Bettas fins (so no tiger barbs).
I've only ever kept one at a time, so no idea about breeding- they may be difficult to breed.
If you want more specifics on suitable tanks/filters/whatever then say so... I've only written some very vague basics here!