painting over green "drywall"?

You would prime and paint it like you would any other type of drywall. You should use an acrylic undercoater and finish with 2 coats of an acrylic eggshell which will hold better in a high moisture area than a flat will.

Green drywall is the same for painting as normal drywall. The green is not, say, a water-repellant dye in the outer paper. The green color merely is the industry standard for signifying that the inside board is made with more water-resistant gypsum materials than ordinary drywall. (If you notice a cross-section, the inside is brownish in color, as opposed to white; but you can't see that cross-section when it is on the wall, so they use green paper.)

It also is a GOOD idea to have it in, say, a bathroom or a kitchen even where you do not have tile so that it can resist moisture or steam. The builder would probably snicker a bit at you if you made that request. :-) He could use it throughout your house with no problem; it would just be more expensive.