To paint you miniatures, you'll have to prepare them a bit, especially if you want the paint to withstand handling while playing the game itself. After assembling your miniature, make sure you wash your miniatures with dishwasher soap and a small bush like an extra old toothbrush. Let them dry completely. After they've dried, you'll first want to coat the miniatures with a layer of primer. Primer is a special kind of paint that is designed to adhere very well to a surface to prepare it for future layers of paint.
I should mention that most gaming/hobby shops should have both paint and primers to use. Avoid using actual GW products as they overprice everything.
Follow the directions on the primer, try to get good coverage of the miniature at all angles, but avoid putting on too thick to prevent it from covering up detail on the miniature.
After its primed, you can start putting on the paint. I'd recommend using acrylic paints, not the testors stuff as those enamel based. Most modeling paint made for gaming miniatures are acrylic. Get yourself a small palette with wells for paint. Put in a small amount of paint in each well of whatever colors you want to use, then add a drop of water to each and stir. The drop of water will thin the paint and make it easier to work with. There are other mixtures you can use to thin paints, and you can even apply the paint straight on the miniature, but for now just use water to keep things simple. Depending on the brand of paint you get you can skip the extra thinner.
You'll want to paint in steps and layers. Start with the base color of your model, the color that is the most prevalent and best represents the lowest layer of paint on the model. For example, if you were doing Blood Angels/Ravens, you would use their particular red almost everywhere on the model. As you apply this first coat of paint, you can afford to be a little sloppier than usual, just make sure you have coverage and get into some of the deeper crevasses. After that initial layer, you can then add on other colors.
Keep in mind that you'll often need to apply multiple layers of the same color to get the color to look proper and solid, this is normal.
This should get you models that are pretty basically painted with solor colors, looking a bit cartoonish with no detail. Don't fret, this is just stage one. In fact, you could just play with the models as is, but if you want your models to look good you'll have to learn how to add shadows, highlights, use washes to put detail into crevasses.