Toilet handles stick when the plastic part that holds the handle in the normal, stationary position breaks or becomes very worn. To solve the problem, replace the toilet handle by removing the old handle mechanism from the toilet tank, unscrewing the old handle and attaching a new one.
Start this repair by turning off the water supply valve that leads to the toilet. Flush the toilet to remove the water from the toilet tank. Toilet repairs are easier in a dry environment. Open the tank, and unhook the chain that attaches the handle mechanism to the rest of the flushing mechanism. Detach the nut on the backside of the handle with pliers or an adjustable wrench to allow the handle mechanism to be pulled through to the outside of the tank. Then unscrew the handle from the handle mechanism, and screw on the new one.
With older handles, it may not be possible to buy a replacement. In this case, simply replace the entire handle mechanism. These are interchangeable, and modern replacements usually consist of plastic parts that do not corrode in a wet environment. Insert the new handle mechanism through the hole in the tank. Attach with the nut, and attach the chain to the arm. Turn on the water to refill the toilet tank.