There are various ways to change the color of polymer clays (**see below for note about the original boxed "Sculpey").
You can add color to the top of it after it's cured/baked, or you can color the "body" of the clay while it's raw before shaping it --or both.

If you mix paint or other colorants into the clay to color it while raw, you *should not* use any which contain water (like acrylic paints--though you might get away with adding only a little).
You'd want to use artists' oil paints or alcohol inks, or you could use powdered pigments and other inclusions like the shavings from oil pastels or mica powders like Pearl Ex/etc or ground spices, etc.

If you want to paint "on top" of the cured clay, the most common paint used is acrylic paint (usually two coats, or one coat of gesso then one coat of acrylic --after the surface has been degreased).
Oil paints can be used but they'll take a long time to dry, and there are some acrylic simulations of oil paint, perhaps needing to be heated to harden, that can be used.
Alcohol inks (like Adirondack or Pinata) work well too but have a less-thick look.
Other "paints"can be created by coloring clear mediums in various ways too.

What you *don't* want to use on baked polymer clay is any paint or clear finish that has a petroleum-based solvent in it (those clean up with paint thinner, and are are sometimes called "enamels"), and some spray paints or finishes which otherwise are fine may have the bad stuff only in their propellants. Those materials will eventually begin dissolving the clay, making it sticky or worse, but it may not happen immediately.

Sometimes paints are "re-baked" after using on baked clay clay for certain effects and will be fine used that way. For example, "antiquing" a dimensional surface usually means applying an acrylic paint all over a surface then wiping the paint off just the upper portions leaving the paint in the lower areas (which creates a more dimensional look or a more "aged" appearance). Clear finishes are sometimes rebaked too after drying just to make them even "harder."
Sometimes "washes" of acrylic or other paints are used on raw clay for lips/eyes/etc, but sometimes afterward instead.

(Btw, if you want a glossy surface on your paint or clay, many acrylics will naturally dry glossy, but if not you can always add a coat of water-based clear finish on top of the clay or the paint to give it gloss.)

There is much more info about which paints and other colorants to use with polymer clay, as well as which sealers/finishes, on these pages of my polymer clay "encyclopedia" site:
http://glassattic.com/polymer/paints.htm
http://glassattic.com/polymer/letters_inks.htm
http://glassattic.com/polymer/finishes.htm
And these pages deal with other ways to create color in or on polymer clay:
http://glassattic.com/polymer/inclusions.htm
http://glassattic.com/polymer/color.htm

**be aware that Sculpey (the boxed, "original" version) is the weakest brand/line of polymer clay so it will not be strong after baking in any thin or projecting areas... SuperSculpey-flesh and Sculpey III are a bit stronger, but not as strong as all the other brands/lines (with FimoSoft being in-between)
You might want to check out at least these pages for more on the various brands of polymer clay, as well as "sculpting" with it:
http://glassattic.com/polymer/Characteristics.htm
http://glassattic.com/polymer/sculpture.htm

HTH,

Diane B.