Baths get blocked when too much material collects beneath the drain. This is generally a mixture of hair, oils and soap.
The wrong way to unblock a bath plug
Traditionally people would clear it with a bent wire (and old clothes hanger was always the tool of choice when i was a lad).
if you have a pastic wasterpipe, then scratching it with a coathanger as you try to clear the blockage can lead to burrs where hairs can collect in future, leading to a repeat of the problem.
You may be tempted to unscrew the plughole cover for easier access, but the screw holds the wastepipe in place, so if you do this then the bathfull of dirty water is going to run all over the floorboards beneath the bath, which could cost a fortune to fix. Leave the screw in the plughole well alone.
Unblocking a bath plug using solvents
Another method to fix a blocked bath is to use a chemical solvent that will wash away the gunk. This is the one the companies try to sell us because the profits for them are huge. However, these are usually very harsh chemicals which do untold damage to the environment and could harm you if you are not very careful when using them. Best avoided except as a last resort.
You could try a bit of vinegar yourself if the bath is empty. Vinegar is an acid and will eat away soapy deposits, grime and hairs overnight.
jet action bath plunger for unblocking drainsIn my opinion plungers are a much better option.
There are two types of bath plunger and both work well. A simple suction plunger creates a vacum and so pulls gunk back up, to dislodge it.
A high pressure plunger looks like a thick bicycle pump and once filled, pumps a jet of water down into the plughole to clear the blockage.
However both methods often force water up the overflow tube, so generally you get nasty residues flying out of the overflow. Stuff this with a rag to avoid getting splattered.