Shut off the power to the garbage disposal before examining it. Never work on a garbage disposal that is turned on.
Use tongs to reach into the disposal so you can pull out anything that should not be in there, like a fork or chicken bone, and remove anything that could have gotten stuck.
Open the cabinet under the sink so you can reach the main garbage disposal unit.
Push the reset button on the bottom of the unit. They are standard on nearly all garbage disposal models and this will solve many problems.
Check the breaker leading to the garbage disposal if it will still not turn on. Look at your breaker box to see if a circuit was shut off. This is more likely if you also notice lights or other appliances not working. Flip the switch that is off in the breaker back into the "on" position to match the others. If it shuts off again right away, you have a short or an overload and should call an electrician.
Listen for a humming sound when you turn the disposal on. If you hear a humming noise and the disposal is still not working, turn it off immediately. Insert a broom stick or another long, thin object into the drain to try to dislodge the flywheel that is likely stuck. Make sure the disposal is not turned on before doing this.
Stick an offset wrench, which should have come with the unit, into the opening at the bottom of the disposal unit and turn it to try to dislodge a stuck flywheel.
Check the pipes and the bolts for any signs of leaking. If there is water coming from under the sink, the bolts on the disposal may need tightening with a wrench or a pipe may need repair.