There are several reasons that a dishwasher will not drain:
A clogged air gap. An air gap problem is very simple to locate and correct.
Clogged Air Gap
A clog in the drain line can take some time only because of accessibility. Emptying the cabinet alone may take 10 minutes. First, check for an obvious kink or clog. Sometimes they are very hard to spot. The best way to confirm a clogged hose is to install an alternate drain hose and try it.
Disposer Knock Out Plug - Needed only when there is no Dishwasher Drain Hose
Trick of the Trade: Occasionally a dofus will forget to knock out the plug when installing a new disposer. The wife says," My dishwasher worked fine until my husband installed a new disposer." Duh! Knock out the plug and collect your money.
Bypass Temporary Drain Hose
A piece of transparent plastic or bone sliver may be flipping around and driving you nuts. You may find that it is handy to have a drill motor pump available to drain the dishwasher (and washers).
If the first two possibities check negative, then it's off to the pump. A pump problem may take some time. New designs have a separate pump motor like washers and they do clog. Access is the issue and may well require pulling the dishwasher out of the cabinet. Most short service port models require complete removal.
Bosch with Limited Front Access
The little pump motor can sit jammed with debris and not burn up. Once unclogged it will be fine. Occassionally a pump will hum and still not pump and need replacement. Bosch is known for weak and troublesome pumps. See the following samples.
Bosch Pump
Kitchen Aid Pump