How do I repaint my kitchen cabinets?
I have painted my share of cabinets - at least 20 kitchens.


Clean everything - I personally use SOS pads because it scratches through oil build up and just knocks things out.  Wipe up excess soap with wet towel.
Sand - a rough grit.  The worse/thicker your old paint the thicker the grit.  You will get advice on stripping the cabinets - don't.  Not unless the paint is "loose" almost everywhere.  And if the paint is "loose" it is usually a moisture problem or really cheap cabinets.  This is a quick sanding too.  A typical 20 year old mid size kitchen would take maybe 1-2 hours to go over.  You are looking to take care of flakes and uneven surfaces.  If there is a lot of flaking sometimes taking a wallpaper remover blade to the cabinets is faster then a quick sand.
Assess the doors and insides.  While sanding you can get a good idea for how the doors could turn out after painting.  There is no magic to fix cheap/rough doors.  Also if doors have ornamental designs or routed lines these are very hard to paint well - almost impossible to hand paint well.  If you need new doors I highly suggest rawdoors.net (no affiliation just a very happy customer with many orders).  You get solid hardwood doors with hinges in lots of different wood flavors and you pick the exact size of doors you want - with older kitchens you can often get a more modern look by upping the door sizes.  On the insides of the cabinets - you don't have to paint or even repaint these.  First if they are the big box cheap laminate looking crap painting them will take forever - they have a clear coat that most primers don't even stick well to.   If it was painted before I wouldn't repaint unless the color is awful or paint is deteriorating. 
Buy your primer and paint.  I highly highly suggest using oil based semi-gloss.  You can go latex but I have found that it has a very rubbery look and just doesn't look good on kitchen cabinets.  Your primer is based on your paint choice.
Thin coat of primer on everything you are painting.  I normally would use a small foam roller for all painting with cabinets.  It keeps the finish smoother and less drips.  Spraying is an option too.  There is usually flooring or something in the kitchen I don't want to get paint on and I have had no luck in keeping spray dots from hitting things sometimes 10 feet away.  Unless I can take the cabinet/doors outside or I am doing a complete gut job, I roll not spray.
Fine grit sanding.
Second coat of primer.
Paint.
Second coat of paint.
I paint the door fronts again once they are installed - and hit any blemishes.  
Optional - clear coat the outside of the cabinets and doors.  


Color...  Almost always a fancy off-white.  I tell the paint store what backsplash and what color the walls will be and they pick out a white that looks like a slight variation of... white.  I have no design ability and I an usually looking to please the general population so the white variations work.  

The last kitchen I did I installed a mid sized island (used cheap lowers from Lowes at $120 total), primer/paint $160, all new doors/drawers - about 30 - (including the island cabinets) $750, and new door knobs $40.  So the whole kitchen cabinets looked brand new plus island for a little more than 1k.  This is labor intensive but anyone can do it.