The IKEA hinges are one of the greatest parts of IKEA cabinets, IMO.  They are Blum hinges, proprietary to IKEA, but Blum nonetheless.   The doors are as easy to remove as they are to install -- we've done so several times for one reason or another.  Door hinges come in 2 packs or 3 packs depending on your door size.  This is a 39" wall cabinet and it has 2 hinges. 

Here goes: On the inside of the door, you'll see the holes for the cup of the hinges (Photo #1).  On the inside of the wall cabinet, you'll attach the cabinet wall attachment point by aligning it with the correct holes (holes #2 and #3 on a 2 hinge door) and screwing the screws into the holes (Photo #2).  Place the hinge cup into the hinge cup hole on the door, aligning the posts with the small holes on the sides (Photo #3).  Press the hinge into the hole (Photo #4).  Flipping the hinge "door" down expands the hinge into the hole, securing it in place (Photo #5).  When both hinges and attachment points are in place, align the bar on the hinge with the hooks on the cabinet wall piece (Photo #6), and snap it closed (Photo #7).  That's it!