Clean first. Sand everything to remove the gloss, or down to bare wood, fill the wood grain with a filling product if it's deep (like err... wonderful open grain oak), sand the filler smooth, clean again. Power tools will help you from going insane.
Sandable primer if you need some extra help or if the grain is not deep enough to need filler. Prime and paint. Use good paint. Use a spray gun, backroll after using a brush, whatever. Experiment with the paint and the paint technique first, so you can remove and try again until you like the results.
By the time it's done the way you want it, it's going to be a few weeks of spare time between sanding/filling, priming, painting, letting everything dry before reinstalling, etc. I've helped people do this before, and it takes quite a while for it to turn out well. If you rush it, you'll do it twice because you'll notice flaws every time you go into the kitchen (or bathroom in this case).
It's also the time to change hardware, because you can fill holes and drill new ones.
We thought about doing this in our house, but we have a few warped doors that are the closest to the kitchen windows and having them painted anything but dark colors will just highlight the twisty gaps even more. We'll just wait until the future kitchen remodel when the cabinets will follow the white formica counters out the door and to the dump.