A well-used bathtub is bound to get clogged every once in a while as hair, soap and the odd stray item form into a glob inside the P-trap. You can often remove such blockages with a plunger, but when you can't, you need an auger. If your tub drain has a crosspiece, you'll have to remove that before you can get the auger into the drain. It looks like a tough job, but it isn't. Two special tools make removal easy, but you may get lucky and not need either one of them.
Wedge a long screwdriver inside the crosspiece and use it as a lever to turn it counterclockwise. If it turns, unscrew and remove the crosspiece, and the job is done.
Turn a pair of adjustable pliers upside down and insert the handles into the crosspiece if you can't turn it with the screwdriver. Weave the shank of the screwdriver through the handles and try turning the pliers like a corkscrew to unscrew the crosspiece.
Rent or buy a drain key to remove the crosspiece if you can't do it with the pliers. Insert the key into the drain opening with the drive screw facing up. Turn the screw counterclockwise as far as it will go by hand. This makes the bottom of the key tighten against the sides of the drain.
Grip the screw with a wrench and keep turning. The key will wedge against the drain, and eventually the crosspiece will begin to turn. Unscrew it all the way and remove it.