Stripping Old Grips
Usually a club repairer will use a sharp knife to remove the old grips before installing the new ones. If you don't have one, you can use a razor blade to cut the grips their entire length before removing them.
Most instructions on replacing grips call for applying "double-sided grip tape" to your shafts before putting on the new grips. If you cannot find this specialized tape, you can also use double-sided carpet tape. It is a little thicker than conventional grip tape, but you will not know the difference once the grips are in place.
Grip Solvent Substitutes
If you were to visit a place like a pro shop or a sporting goods store where they repair clubs, you would see gallons of grip solvent used in the grip replacement process. If you decide to re-grip shafts yourself, and grip solvent cannot be found, you can use lighter fluid or acetone, which people use to remove nail polish. As with any solvent, use in a well-ventilated area away from open flames, including cigarettes and cigars.
Speed Up The Drying Process
Most instructions suggest you wait about 24 hours before using your clubs after re-gripping to give them a chance to dry. If you need to use them earlier, use a hair dryer on your grips to accelerate the drying process.