If your garbage disposal is clogged, there are a number of steps that you will need to take in order to fix the problem safely and properly.
The first and most important thing to keep in mind is to never, under any circumstances, put your fingers in the garbage disposal. Even if you think that it is a small clog or that you only need to move a small piece of debris, do not put your fingers in the garbage disposal.
The phrase “better safe than sorry” exists for a reason.
The best thing to do is to go to your circuit breaker and shut off the circuit connected to the garbage disposal. You should test the wall switch to ensure that the proper circuit has been shut off. Next, grab a pair of tongs or whatever you can find that is long enough to reach the disposal without putting your fingers at risk. Attempt to remove any debris that may be blocking the drain. Run the sink a few times and probe the area to see if there is still a blockage. If water is still not draining properly, turn the circuit back on and run the disposal in a few short bursts. This should free up the drain if the clog is at the disposal.
If you are confident that the disposal is clear and that the source of the clog is further down the drain you should call a professional plumber. It is not advisable to use a plunger on a drain with a garbage disposal as the pressure may damage the disposal. A plumber will be able to diagnose why your garbage disposal clogged and clear the drain. The plumber will also be able to replace the garbage disposal and recommend the proper sized replacement if that is the problem.