A screwdriver will do. You'll want a Phillips, the wider the better.
Take a towel and put it on a cutting board. Lay the oyster flat side UP on the towel, then wrap the towel over it, leaving the hinge exposed. Rock the oyster back a bit so the hinge is pointed up, and hold it firmly in that position. Insert the screwdriver into the hinge; you should be at an angle where a slip will end up with the screwdriver hitting the towel and board rather than your fingers. While pushing in firmly, but NOT as hard as you can, push the point of the screwdriver down and twist it slightly against the hinge. You should hear or feel a bit of a pop as the hinge releases. It can take a few tries to get the feel for it if you haven't done this before.
Cutting the muscle loose may be a bit tricky with a screwdriver, but it should be managable. This is actually where you're most likely to damage the oyster, so be careful.