To unclog a drain with a disposal unit, Family Handyman recommends first using a plunger to loosen the clog and force the material down the drain. Another way to clear a clog is to disconnect the drain trap connected to the disposal and clean it out. If that doesn't work, Bob Formisano of About Home Repair explains an auger can clean out a clog beyond the drain trap.
If the garbage disposal makes a low humming sound when it is first turned on, Family Handyman states the cause is probably a jam. Switch the disposal off and unplug the unit before using an Allen wrench to turn the blades. If a dishwasher is connected to the disposal, clamp the flexible part of the drain before plunging to prevent dirty water from going into the dishwasher. Sometimes, a breaker automatically shuts down the disposal after the motor gets too hot. If this happens, give the unit a moment to cool before pressing the reset button on the bottom.
Some plumbing chemicals are safe to use with garbage disposal clogs. Items that commonly clog drains with garbage disposals include potato skins, banana peels, coffee grounds and eggshells. Drano states grease and oil can stick to the inside of pipes because these substances do not get broken up by garbage disposals. Applying drain chemicals augments the unclogging process.