I've been painting for a long time now. Here's a (believe it or not) brief breakdown of the process:
Before anything else, you want to hit a well stocked nerd-shop, if possible. You're gonna need some tools. (If you've got no hobby shop, gamer store, or model train store around, a trip to the hardware store and a bit of internet shopping does just fine).
Xacto knife. Just the standard model, usually comes with a few "no.11" blades.
Small files and/or very fine sandpaper.
A spray-can of Black model primer. "Armory" and "Citadel" (Games Workshop) make good Black primers available at most game shops. "Model Masters" do as well, and are often available where model car and train kits are sold. White primer is also an option, as is Gesso, but you'll likely need to work up to these. They tend to be more tricky and much less forgiving than Black.
Decent mini brushes. Don't go crazy buying super-nice brushes until you're pretty confident in their use. You will ruin your first several brushes over time. Get a small cake of brush cleaner (for Acrylics) if you find it, and have the spare cash.
Vallejo brand paints. These are fantastic, inexpensive, and come in "eye-dropper" style bottles that save a lot of time and money in the long run. Get your four Primary colors, Black, White, and anything else that strikes your fancy. I highly recommend getting a few flesh tones. Mixing them from primaries can be tedious. The Talisman characters (if you want them to look remotely like the images on the cards) have quite a bit of Green, Purple, and Brown going on. You may want to get a few shades of those if you've got the money on hand. Vallejo Inks are also recommended (Green, Purple, Brown, etc.), but not totally necessary for a reasonable paint job.
A spray-can of clear-coat. Same brands as listed above for "Primers" should be just fine. Decide on Matte or Gloss. Matte retains more of the feel and color of the paint, but offers a bit less protection for the finished mini. Gloss does just what it says. It leaves a hard shiny coat over the finished model, more durable that matte, in general.
The actual process:
1. Clean up the minis with an Xacto knife, small files, and/or very fine sandpaper. You want to get rid of any extra plastic left over from the molding process. Careful, young Jedi, some of the Talisman figures have little details that can fly right off should you get carried away. (A "cardless" Gypsy is no Gypsy, at all.)
2. Wash them up a bit (finger grease can be a real pain for priming / painting), let them dry completely, then take little a bit of Blu-tac (poster putty), a tiny amount of plain White Glue, or even a very (very) small amount of chewing gum, and stick several of the minis on piece of carboard (standing up). You'll want four or five inches between them, in a row, as you'll be spraying them on the cardbaord this way.
3. Take the cardboard tray of minis outside. Shake the holy hell out of your can, and spray them with the Black primer. Spray in several, thin, even, coats. Let dry totally between coats. At least a half hour between coats. Two or three light coats should more than do it. Too much primer in one spray will puddle up, drip, run, and actually fill in the fine details of the mini. If you find that you've missed a few "hard-to-spray" spots, don't sweat it, don't keep spraying the whole thing just to get behind a shield or under a cape. You can wait till the minis are dry, then touch up those spots with a bit of black paint.
4. Once the models are totally dry (I'll often let them sit overnight, just to be sure) you now have "Primed" minis, ready to go. You'll notice that there is now a very fine grainy texture to the minis. That's what primer does. The paint now has a bit more to cling to. It should be a very, very fine texture, however. If you see bigger chunks, or the minis visibly look like sandpaper, you probably didn't shake th can well enough (or got a bad can). You'll have to strip the minis, and head on back to square one. (I'll get to stripping here in a bit). Once you're satistfied that they're dry, take them gently from the cardboard, and mount them (again with a little Blu-tac or something) on plastic soda-bottle caps, or something similar. This will give you something to handle (other than the figure itself) when painting.
5. Paint your base colors. If a cape is hues of Blue, get out the darkest Blue and carefully paint it in smooth, even, light coats. Like the primer, you will need a few light coats to do this right the first time. You'll cover the whole surface of the cape in this darkest Blue. Later, once you've done the base colors for the whole model, you'll go back and add the lighter colors and highlights that give the colors depth.
6. "Layering-up" from dark to light. You can often achieve a pretty decent layering effect by simply adding a little bit of White to your base color. When you think of it in terms of the draped folds of a Blue cape, think of it in three simple layers: First, Dark Blue, over the whole cape. Second, a slightly lighter Blue, covering just the curves and folds blowing "outward", away from the mini's body. Third: an even lighter Blue, going in almost a thin stripe down the center of the blowing folds. The trick to this is finding a comfortable middle-ground between each of your highlights. If the Blues are too similar, the effect is negated, if they're too drastically different or too bright, they'll look like stripes printed or painted on the cape. Remeber: when mixing colors, "not enough White" can be fixed easily: let it dry, add a bit more white to your color, try again. "Too much White" means you may have to cover the whole area in your Darkest shade again, and start over. Start over too many times, and the model begins to lose detail for all the paint thickening upon it.
7. Details. Now is when you pull out the tiniest brushes and do the tiniest bits. Buttons on coats, eyes, weapons, whatever. This is the stage that chases many folks away from the hobby. They don't get it right the first time, so they assume the second time will be a bust, too. The internet is a goldmine, my freind, google "miniature painting", and look at the techniques different people use for fine detail. Make note of the best. Practice, practice.
8. When you're happy with the mini, let it dry well. Then, you're going to shake the hell out of the Clear Coat can and spray it in even gentler, thinner coats than the primer, letting each coat totally, totally dry. I can't stress that enough. If you soak it, your whole paint job will look like shiny, glossy, crap. Also, watch the weather. If its too hot and humid, or damp at all, your clear coat may "fog". It is just what it sounds like. A murky film will magically appear over your proud new paint job.
There are, of course, a great many more things and techniques you can try, but those are the basics. There's a lot of trial and error, and a lot of patience. Here's a few simple tips:
Assembly Line: With something like a Talisman set, you have the luxury of getting a lot of mini's at once. So paint them at once. That is to say, clean and prime them on the same day. Prime them in a few groups of four or five. Get out your character cards and break them out in groups of "These quys all have a lot of Green" and "These use a bunch of Blue", etc. You can do the base colors on one "Green" character, and move on to another while it dries. This will save you a lot of time, and keep things moving. You'll also likely see a few things you did "wrong" on one model, and be able to correct it on the next.
Layering and Highlights: I gave a simple example of Three layers. This is by no means a limit. Once you get the hang of color theory and blending, sky's the limit. Just don't put too much time into your mini's when doing a whole set, especially one that's gonna get played with, dropped, and potato-chip-fingered like a properly used Talisman set surely will.
Fleshtones and Hair: These can be problematic for new painters. Save yourself some time and drama by just buying a few different fleshtones / standard hair colors. Get ones that will "layer up" easily, so you don't spend a lot of time mixing and layering them for each figure.
Inks and Washes: These are often used to bring out details in a figure or to enhance their colors. A "simple" tutorial on their various uses and aplication techniques would make this missive look tiny. Do some research. You can use ink and washes to cut corners, or accentuate a prize worthy paintjob. Here's my only contribution to the process: Dish Soap. Get Googling. Someone else has surely stumbled upon it, as well.
Basing: If you want to add a nice touch to any mini you paint, get some "ballast" and/or "static grass" from a hobby store. These give texture and scenery to the the "ground" your model stands on. They're often super-easy to apply, and can make the difference between a cool mini and an awesome one.
Stripping old paint: If you purchase an old model that someone painted poorly, or you've passed the point of no return with one of your own, you can strip it. There are many suggestions from many sources about how "best" to do this - but here's one that works. "Super Clean". It's a degreaser sold in many auto parts stores. It's a massive purple bottle. You can get one for five or six USD in most megamart-type stores. Pour a few inches in a bucket, dump in the mini, let it soak. Then, get some gloves, an old toothbrush and go nuts. You can soak metal minis forever, plastic should be monitored, though. Softer plastics like the Talisman minis may begin to soften further if left in the purple soak for too long.
Practice: If you'd like your Talisman figures to look like a coherent set, and not necessarily like a visual progression of your ever improving painting skills, grab a few cheap minis at a game shop or online to play with first. It's like anything else that takes practice: Your first few mini's will likely suck. Possibly hard. Do you want them to be your Assassin or Sorceress, or some random plastic Warhammer dwarf you got in a bargain bin? Hell, should you turn out to be a natural, your little plastic dwarf will come out fantastic, and you wind up with "Thwakax: Chopper of Knees". Roll up some stats, make him a card, and unleash him upon the Talisman board.
Too much information for a simple question? Probably. Enough info to answer all of a freshmen painters concerns: Not likely.