Gen stained doors have a clear finish. Depending on the type would make it easier to figure. Basically you need to dull the surface by either using sand paper in order to apply a bonding primer in order to paint. Another thing you want to be sure of is the type of product used. Is the finish oil of latex? Gen an oil primer will work either way. But latex paint over an existing oil finish will not work.
So in a nut shell, sand well, apply oil primer and paint with oil or latex.