I used to do this, and don't really have time to anymore.
There are a lot of different methods, but most of all, you need to finish cleaning up the seams and perhaps carve some details (usually Breyers have lots of mold seams/flaws, and they don't do such things as carve out the ears, or the hooves, etc.) and make sure the finish is as smooth as possible.
Prime it depending on what you'll be using for a color and type of paint (you can use oils or acrylics, brush or airbrush), keeping it nice and smooth.
Then begin your paint job and go from there.
There are lots of websites and informative email lists out there to help you learn.
It's fun to do and really enjoyable to have those finished products in the colors you want them to be.
Have a look at some of the artists resins being made (blank bodies that are ready to be finished/painted by you or another artist as you want them to be).
Some of my favorite artists are:
http://www.riorondo.com/
http://www.rosehorse.com/
http://www.lafnbear.com/
http://www.mink-studios.com/
I have some resins from all of the above, and I really enjoy them.
Liz M.