One of the easiest paints to use is the acrylic paint sold at most craft stores. There are several brands, but Ceramcoat is the one that pops into mind - personally, I think they're all about the same. Many colors to choose from, so you don't have to do much color-mixing if you don't want to. I usually dilute my paint with water, say five drops water to one of paint for the darker colors, and two drops of water to one of paint for the lighter colors. If the color isn't intense enough, another coat a half hour later will usually take care of that. Ceramcoat also makes a water-based varnish, in both satin and gloss finish, to use, as well. Cleanup is easy. The primary reason I dilute the colors is because I prefer the paint to be a wash coat, not a solid opaque color - I like the wood grain to show through. Choice is up to you though, depending on how you like it. I also usually put a coat of Minwax oil-based sealer on the carving first - let it dry for a week, then paint. The acrylics will soak instantly into the wood if it hasn't been sealed.
Many carvers prefer to use artist's oil-based paints. You can get some wonderful effects with these, since they don't dry almost instantly - they're easier to blend the transition from one color to another so it looks natural and not like a paint-by-numbers.
I've now told you twice as much as I know, so I'll quit with one final bit of advice: use one of the scrap pieces of wood you have laying around and try the paints on the scrap first, then put on your carving if you like the look.