Sometimes unclogging a bathtub can be as simple as using a toilet plunger on the drain in order to get the water flowing again. The best way to do this is as follows:
Wear some rubber boot if you have them in order to prevent slippage. It wouldn’t hurt to wear eye-goggles either to prevent dirty water from getting into your eyes.
Remove any standing water using a bucket or cup.
Remove the strainer or stopper that may be in the drain. This can usually be done using a screwdriver.
Add a few inches of water to the tub. You will need this for the plunging-suction action.
Use your toilet plunger to push and pull liquid into the blocked area. This action can often loosen the material that is causing the drain clog.
If any debris comes back into the tub, make sure to remove it.
Repeat sever times until the drain is moving water again.
If this does not work then you can try using a snake or auger. This device comes in handy when it is time to get at really tough blockages. Many blockages are caused by a combination of hair and soap residue. The auger will punch right through that type of clog.
If the methods above do not work, you may need to call a professional plumber. There could be a bigger issue at hand and the sooner your plumber can diagnose this problem the better.