It isn't unusual for all the plumbing fixtures in a bathroom to empty into a common waste line, and the bathtub drain is usually the lowest of any of them. Consequently, if there's a blockage, and water starts backing up, that's the first place from which it will emerge. You'll probably notice the toilet flushing poorly at the same time as this is happening. Like any toilet drain blockage, you should be able to clear it with a plunger, but there's a trick you should know first. Using it will make it more likely that plunging will work.
Step 1
Wrap duct tape around the bathtub trip lever. This covers the overflow opening and makes the plumbing pipes airtight. Cover the overflow holes on the sink in the same way. If there's a shower in the bathroom, lay tape over the drain.
Step 2
Flush the toilet or pour water into it to make water come out of the bathtub drain. Close the drain stopper or put in the drain plug. Do the same in the bathroom sink.
Step 3
Fit a plunger around the waste outlet of the toilet bowl and pump it vigorously a few times. This may be enough to clear the blockage. Try flushing the toilet to see if the flush has improved. Plunge again if it hasn't.
Step 4
Check the tape you applied and stick it back down if it came off. You may have to fortify it with another layer. Try plunging again.
Step 5
Use a toilet auger to clear the blockage if plunging has no effect. Wearing rubber gloves, insert the auger through the toilet and push it in until you encounter resistance. Crank the auger handle to work the head through the obstruction. Pull the auger out periodically to clean the head.
Step 6
Insert the auger through a cleanout if it can't reach the obstruction from the toilet. You should be able to find a cleanout near the toilet. You may have to go into a closet in an adjoining room to access it. It has a screw-on cap that you remove with a wrench.