Ensure that the disposal is unplugged from the wall or that the power to it is turned off at your home's electrical control panel (breaker box). Use a noncontact circuit tester to verify that no power is flowing to the device. Then, with a flashlight, look down inside the disposal. If there's something inside of it causing the clog, use a pair of long, needle-nose pliers to reach into the disposal to retrieve it.
If the clog is within the garbage disposal chamber, in should be easy to fix. Your disposal should have come with an Allen wrench (also called a hex key or hex wrench). If it's missing, you can pick one up from a hardware store that sells your brand of disposal. Or you may have the right size Allen wrench in your tool box. The Allen wrench fits into a hole that's at the center of the bottom of the disposal. With the power disconnected, insert the wrench into the hole and twist it back and forth. You'll feel slight resistance at first, but it should turn freely once the clog is cleared. Press the small reset button near the center hole. It's usually red. Restore power to the disposal and turn it on. You might have to repeat this process several times before the clog is cleared.
If no Allen wrench is available and you can't go to the hardware store to get one, you can try using a sturdy dowel, wooden spoon or broom handle. Again, ensure that the disposal is off and disconnected. Insert the dowel into the opening. Do not insert your hand. Your hand should be well above the opening of the disposal for safety and leverage. Push the dowel against the disposal's impellers (the blades that grind the garbage), and rock it back and forth. You can expect to encounter resistance and will need to use a moderate degree of force. When the impellers move freely, press the reset button on the bottom of the disposal, restore power to the disposal and test it to see if the clog has cleared.
If the clog isn't in the disposal itself, you may have a clog inside the drains. Try using a new, clean plunger in the basin without the disposal to dislodge the clog. If that doesn't work, you will need to get under the sink and disassemble the drain pipes. Start with the drain closest to the disposal and work your way to where the drain pipes meet the wall. Position a bucket under the drains where you're working to catch any spills.
If the disposal remains clogged and you're still hearing a gurgling sound, the problem may be with the disposal itself or further down the drain pipes. Garbage disposals aren't difficult to replace, but it does take about an afternoon. Or, you could try to run a 25-foot auger snake further down your drains to see if you can clear any clogs. You can either rent or purchase auger snakes. If both of those options are beyond your skill level, it's time to call a plumber in to assess the problem.