I just started painting these myself (after a 20 year gap).
Best advice i can give (though maybe not the best advice you can get) is....
Get some acrylic paints, the warhammer ones are good, or any others will do. Im actually using some really cheap ones from a kids paint set, i just mix colours to get what i want. I also have some Warhammer ones from the "Lord of the Rings" Goblin starter set, which also includes a brush and 10 or so little Goblins to practice with
If its not the Warhammer ones then use a few drops of water to thin them a little before you start.
Paint all black to start with (or white depending on the colours, white seems to be good for brighter coloured figures, though black seems to suit just about everything).
Keep the paint thin and dont use too much paint, less is more.
Once dry start adding colours, large areas first.
I use drybrushing a lot, this is where you coat the brush then gently stroke the brush over some kitchen paper to wipe the excess paint off (almost wiping off most of the paint). Carefully start to cover the area you want with colour, again, keep the paint thin and use as little as possible with each stroke, keeping the brush basically dry means the paint doesnt fill in all the little features.
If you start with a darker shade for the first coat then you can add gradually brighter coats on top, creating a bit of shadow and depth. Use highlights at the end to give a bit of light to the figure, again, just tiny amounts here and there to simulate a light source and shadow.
Once your done and its dry, you can "wash" a coat over the top, this means getting a shade which is dark and a match for the main colour (so for red use dark brown, a dark orange for yellow or whatever you think). Really water the paint down for this, a lot, and add black to make sure its nice and dark. Once its ready (it should be very thin, almost like water), add some to the brush, wipe it off a little then paint over the area (this is good for colouring material, bone, skin) with the dark, watery wash coat. It should settle in the grooves and detail areas giving them more depth and contrast, yet be thin enough it doesnt actually cover the main areas of clour. I sometimes use a little tissue paper to wipe away any excess.
Finish off with a few details such as eyes and metal and your done.
For eyes i sometimes use a pencil dipped in a tiny bit of paint (again wiping off any excess), for metal use mettalic paint, or, as ive done a few times, my girlfriends shiny nail polish
dont know if this is common or not, but ive got some great gold and silver effects using this
Like i said, i dont know if this is the ideal method, but it works for me.
Ive been using the Warhammer brushes, smaller the better, and be careful as the drybrushing technique means the brush wears quickly so buy a few of them
Oh... and if it goes wrong, acrylics are easy to wash off, i use water but apparently pine oil is good (or thinned down pine floor cleaner), a little soapy water seems to work fine though.