Are we talking a vinyl door or a factory finished steel door?
It is not recommended to paint Vinyl. Steel overhead doors can be repainted by simply scrubbing them with a stiff scrub brush and a strong cleaner to remove any chalking. Make sure to rinse them well, then allow to dry overnight and then prime with an adhesion primer. My favorite primer for this is Brunning's "Grabber Plus". Grabber is a latex primer that is easy to use and has incredible adhesion properties. When the primer is dry, paint with a premium grade paint. It would be best to consider using two coats of finish paint.
I personally prefer Benjamin Moore paints. Moorglo or Moorguard are excellent products for exterior applications.