How to paint / decorate both sides of a plasterboard?
Yes, you can paint plasterboard directly - it's usually just paper on the outside. (Moisture resisting plasterboard tends to have a foil on on side though, which probably won't take paint well).

What paint you use will depend what finish (or colours) you want, but you're unlikely to have problems using either emulsion or undercoat and gloss (or matt or eggshell) topcoat.

Here's some information about plasterboard.