[Arran]

One of the first things that you will need is a selection of woodworking clamps, pipe, bar, large C clamps, buy, rent or borrow them. The veneer has started separating because the cabinet was stored improperly in a damp environment at some point, age does not make it separate. One way that I use to glue down loose veneer is a hypodermic needle of a decent size, the ones they include with ink jet cartridge refill kits are perfect for this as as the syringe is over 5/8 in diameter and the needle is 1/16 inch or so. You take the plunger out and fill it with yellow carpenter's glue and inject the glue between the layers, then clamp it between some wooden blocks covered in wax paper or Saran wrap, then wipe up the excess that squeezes out with a damp rag or paper towel. I would do this before stripping the old finish off, it will prevent the glue from staining the wood and you won't get any stripper or crud under the veneer or in the cracks. It also gives you a chance to remove any glue stains while you strip the cabinets so you don't have to go back and do it twice.
Regards
Arran