The first thing you need to get is a spray can of primer, you can pick up one at your local game store (Citadel Brand or Army Painter ) or if you feel like going for cheaper you can get primer spray at home depot/lowes. ( Ive used Rust-o-leum flat black primer for Cars and it works fine.)
I suggest black primer, because when your painting if you miss a spot its harder to see as opposed to white or color primer. The downside to a dark primer is that whatever paints you put on top will come out darker than if you painted on white or color primer, so you might need more layers to achieve a lighter coat of paint on the models.
Your next step is to pick up some paints, I have been a GW purist until now so the paints I use are Citadel Paints, I have seen other folks use Vallejo paints and they look great as well, I just have not tried them yet.
Most gamestores will have the basic paint set, which comes with a couple of brushes and 6 - 7 paints, mostly primary and secondary colors, black and white. I recommend picking one of these sets up just to get you started, also you might want to pick up any other colors you might need, a metallic color for guns and maybe a brown if its not in the set. This is the only thing I never skimp on, if you want your models to look good you need paint made for models.
As far as brushes, if they don't have em at your local game store, or you dont feel like spending the money for one of those, you can try Michaels/Pearl/AC Moore or any other craft store in your area, you can get brushes fairly cheap there
The last thing you'll need is some kind of sealer to make sure the paint wont chip off your models when your playing and whatnot, there are two main kinds of sealer, there is a flat matte sealer or a glossy sealer. I prefer the matte sealer but it tends to dull out metallic paints, while the glossy sealer makes your whole model very shiny. I haven't used sealer on any of my figures yet, just in case i want to touch something up or repaint something but when your happy with how yours came out you can spray em down and your done. Citadel makes a sealer called Purity Seal, not sure how good it is but your local store should carry some kind of sealer, if not you can pick some up at Home Depot as well.
So in essence what I recommend is
Flat black Primer
Beginner Paint set
Couple of small brushes
Matte Sealer.