Run the garbage disposal to remove any remaining food or debris.
Check to see if the knockout plug on the disposal has been removed if you had the unit installed recently. Remove the dishwasher hose where it connects to the disposal. Place the end of a screwdriver against the plug if it is still intact. Tap the end of the screwdriver with a hammer to release the plug. Reach inside the disposal with your fingers or a pair of pliers from above the sink and remove the plug. Reattach the hose to the disposal.
Access the dishwasher drain hose from beneath the sink. Remove any kinks in the hose.
Unclog the air gap, if there is one. Unlatch the dishwasher door. Remove the metal plug protruding from the sink edge on the left side of the kitchen faucet. Unscrew or pull the plastic cap from the diverter inside the plug. Remove any debris and replace the cap and plug.
Unclog the kitchen sink drain with a vinegar and water solution. Wet a rag and set it aside. Stir 1/2 cup of white vinegar and 1/2 cup of baking soda together in a bowl. Pour the solution down the drain. Stuff the rag into the sink drain and wait 10 minutes. Remove the rag and turn on the hot water. Allow the water to run down the drain for three to four minutes.
Unclog the kitchen sink drain with a plunger. Remove the drain basket. Fill the sink halfway with water. If the sink is already filled more than halfway, use a bucket to remove the excess water. Stuff a rag into the drain of a second sink, if you have one. Place a plunger over the drain hole. Press the plunger forcefully 10 to 15 times or until the clog releases and the water drains freely. Remove the rag from the second sink, if applicable.
Descale and disinfect the dishwasher drain system, tub and water lines with white vinegar. Pour two cups of white vinegar into the dishwasher tub. Run the dishwasher through the hottest, longest cycle.