Clean up the cabinets. It's extremely important to make sure your cabinets are free of all grease, grime and food residue before you start painting. The easiest way to do this is to remove all of the cabinet doors, lay them out flat and use an all purpose cleaner and rag. Allow them to dry thoroughly.
Sand the cabinets. Taking the time to lightly sand your cabinets will greatly increase the longevity of your paint job. Use a piece of fine grit sandpaper (150 or finer) and make a few passes over all of the flat surfaces of the doors (don't forget to do the thin facing pieces on the cabinet boxes themselves). Sanding will allow the primer to bite and take hold on the cabinet surface. Don't underestimate the importance of this step!
Apply primer. Now it's time to prime the cabinets. Priming the cabinets means that the paint will be less likely to chip and peel. If you are re-painting your cabinets the same color then it is okay to skip this step. If, however, your cabinets are stained and you are covering up the natural wood grain with paint, you must prime first. Paint will not stick to varnished surfaces and the color of the stain will most likely bleed right through the paint. If you are using an oil-based paint, an interior oil based primer is recommended. Due to their strong odor, make sure you use the primer in a properly ventilated room (such as a garage with the overhead door open). If you are planning to use a latex paint then a shellac based primer is recommended. Be careful, as this primer tends to dry quickly, so make sure you are ready to go before you begin applying it. As with the oil-based primer, this primer carries a very strong odor and caution should be used.
Paint the cabinets. By this point your cabinet doors probably don't look very pretty, but don't worry; now they're ready for the top coats of paint. The best way to apply the paint is a pneumatic sprayer, but if you don't have access to one you can still get a great finish by using a high quality paint brush. 2 1/2" to 3" would be ideal. The key to a professional finish with a brush is to use very thin coats. The best and most durable paint jobs are built by consecutive thin layers of paint. Not just one thick one.
Add additional coats. Let your first coat dry completely. If you want to achieve a truly professional finish, take some 400 grit sandpaper and lightly sand the flat surfaces again. You are not trying to remove the pain, but insuring that the next coat has the smoothest possible surface to adhere too. Two coats of paint will most likely be sufficient. You may need three coats with woods that carry a heavier grain, like oak. Once the doors are painted and dry, simply hang them back up, and enjoy the bright, renewed space that you've worked so hard to achieve.