Do not use water! Most glues used for furniture are not water proof or water resistant. Use water and you have a good chance of breaking the glue bonds and your table will fall apart or at least cause some separation of the joints and weaken the whole table. If it is solid Oak and not a veneer you can use a power sander and carefully sand out the stain, but keep the sander moving so you don't create an uneven surface. You can use hand scrapers if you don't have a sander.
If it is veneer you can use a heat gun to heat the top to break the glues adhesion. Remove the old veneer, strip off the old glue, again heat and a putty knife plus some power sanding or hand scraping. You can buy new veneer at most wood working supply stores (not the box stores).
Use a good quality contact cement and put a coat on the veneer and the table top. Lay sticks or or boards that are the width of the table on the table top on top of the cement. Put your veneer glue side down on top of the sticks. Square up the veneer to the table top then start at one end and pull a stick out. Press the veneer to the table with your hand. Keep repeating this until you have the top and the veneer mated, then use a J roller to ensure you have a good contact with no air bubbles.
Use a router to trim the veneer edge, then use a piece of sand paper or a file to knock off the sharp edge that is left from the trimming. It sounds difficult but if you pick up some books or watch a demo on YouTube you will find it is not that difficult. Good luck, you will have to decide if the table is worth this extra work.