Hi Catherine and welcome to the forum
A lot of doors are finished using what is called a two-pack lacquer which means that conventional caustic dipping won't strip them. The pine stripper actually has to use a special formulation to get the stuff off and as others have said it tends to raise the grain and can sometimes cause joints to fail. I've found that the biggest disadvantage to stripping kitchen doors, however, is that you may be somewhat disappointed by the end result - the doors are often made up from a multitude of timbers of slightly varying hue (natural, but it can still be visually disconcerting) so in it's stripped state your kitchen may end up having a bit of a "harlequin" look which must then be painted to hide it. When the doors are manufactured this is generally disguised by the judicious use of sprayed dark-coloured stains.
I reckon the two main things are to degrease them and then to provide a mechanical "key" for your paint to attach to. I'd recommend that you take the doors off and remove the hinges and handles - most older hinges attach to the cruciform plates inside the cabinet with a single screw and may have a couple of screws each to hold the "pots" onto the door. To degrease use either sugar soap (available from decorators suppliers) or possibly washing soda crystals dissolved in hot water and a dish cloth (don't immerse the door in water), but do remember use rubber gloves as these materials will degrease your skin in next to no time as well! You may need to go over them two or three times or utilise a nail brush (nylon bristles) to get rid of really stubborn grease. Once you've degreased them and allowed them to dry, a light sandpapering with something like 180 to 240 grit sandpaper will scuff the surface enough to provide a key for your paint - you are actually looking for a matt surface to paint onto. Wipe over your sanded surfaces with a rag soaked in white spirits to remove any sanding dust and you're ready to paint.
Scrit