You will want to clean your cabinets very well, and use Krud Kutter to de-grease and de-gloss the surface.
Adding primer is very important! You will want to add 2 coats of primer, lightly sanding with a fine grit sandpaper between coats.
You will then add 2-3 coats of paint using a brush and a foam roller. I used an interior laytex paint with an eggshell sheen.
Apply the same technique to the cabinet bases, using the roller when you can. This gives a smooth finish.