If your tub has a built-in stopper, remove it and check the drain for obstructions. The mechanisms that operate these stoppers can sometimes catch hair and other debris, creating a nasty clog right at the drain opening. A wire coat hanger can help you probe the drain and remove any material that may be blocking the water flow.
Most tubs have an overflow drain mounted above the main drain. This is so that if the water level rises too high, the excess water will flow down into the pipes and not onto the floor of the bathroom. Unfortunately, this also makes it difficult to create a proper seal to maintain pressure. Use duct tape to securely cover the overflow hole.
Once the overflow is sealed, you can use a plunger to try to force the drain open. Press the plunger firmly over the drain, creating as much of a seal as possible, and plunge quickly and firmly. The pressure and suction created by this action should cause the clog to break apart and come loose, restoring water flow through the pipes.