If the stopper isn't the problem, then the drainpipe is probably clogged. First, try a plunger or chemical drain cleaner. If these fail to do the job, you'll have to clear the trap with a snake.
Most tubs have a P trap in the drain.
Using a snake in a tub P trap is much like snaking out a sink trap. If you have a drum trap, first try snaking it clear through the tub overflow. If that doesn't work, bailout all the standing water from the tub. Then, using an adjustable-end wrench, unscrew the trap cover slowly. Have rags ready for any water that wells up.