When a dishwasher won't drain, that usually means that the appliance's drain line is clogged. The drain line, which connects the dishwasher to the garbage disposal, must be cleared of debris before the dishwasher will resume its normal operation. If the drain line is the problem, clearing it is simple and requires only a few standard household products.
Turn off the power to the dishwasher, if possible. Remove all the dishes and the racks. Put on a pair of rubber gloves and use towels to soak up most of the standing water in the bottom of the dishwasher.
Unscrew the rotating sprayer arm in the bottom of the dishwasher. Rinse off the arm and all its seals and screws in the sink and set it aside.
Locate the filter screen in the back of the dishwasher's floor. Pop off the screen, using a screwdriver to loosen any bolts that may be holding it in place. Rinse off the screen, then wipe the dishwasher floor with paper towels to remove any large pieces of food or other debris. Wipe the area clean with a damp sponge.
Replace the screen and the sprayer arm. Locate the drain line; it should be near the back of the floor of the dishwasher, right underneath the filter screen. Pour 1/2 cup baking soda into a cup and add enough water to make it into a pourable paste. Pour the paste into the drain line through the screen. Add 1/2 cup vinegar to the drain line and let the solution fizz for 15 minutes.
Boil a quart of water. Remove the pot from the heat, allow the bubbling to subside and pour the water into the drain line to clear the baking soda solution. Watch the water go down the tube; if it seems to be draining slowly or not at all, repeat the baking soda treatment.
Replace the racks and make sure that everything is put back together properly. Turn the power back on and run the empty dishwasher through one normal cycle to see if the drainage problem is fixed. If not, repeat the process a few more times. If the issue still isn't resolved, the problem may be with the pump or another electronic part. A professional is best suited to deal with an issue like that.