A very common oversight when installing a garbage disposal is forgetting to remove the knock-out plug from the side of the unit. The purpose of the plug is to create a watertight seal in the event you don’t have a dishwasher.
If you have a dishwasher, the drain line connects to an air gap and then drains into a nipple at the side of the disposal. In this nipple is a plug that must be removed so that the drain water will flow freely into the disposal and out of the trap.
If you don’t remove this plug the water will back up into the air gap and onto your counter. If you do not have a dishwasher (and therefore won’t be connecting one to the nipple), you don’t need to do anything to the plug.
If you are connecting a dishwasher to the nipple, you need to remove the plug. If you have forgotten to remove it and the new disposal is already installed, you can remove the drain hose from the nipple and use a screwdriver and a hammer to tap it loose. You risk damaging the sink or the disposal doing this however, so you might want to place someone or something behind it to prevent it from moving do you your hammer strikes. The safest way is to place the disposal on the floor and tap out the plug with a screwdriver and hammer.
Once the screwdriver breaks through, you can either turn the disposal upside down, or reach inside and pull out the plug.