Bathtub clogs are not all that uncommon, but they are sometimes a hassle to unclog. There are many methods to use depending on whom you ask. There are several things you can try before calling a plumber. Of course you can try the traditional methods such as using a plunger, or drain snake. You may choose to pour hot water down the drain, or a combination of baking soda and vinegar. Some methods are a bit unconventional such as using a shop vacuum. There is always the old stand-by of chemical cleaners. The best thing to do is prevent drain clogs in the first place by being careful what you allow to go down the drain, and by cleaning your strainers and drains on a regular basis. If you do get a clog should be able to open the tub drain yourself using one of these methods.
Here are links to some methods you may want to try: