Checking the drain hoses for clogging involves removing them from their connection to the air gap or the house's drain system, and checking for debris clogging the hose or barb fitting.
If you have an air gap in your system, start by checking that. It's a common place for clogging to occur, and pretty easy to get to.
The Air Gap
All the appliances in your house that use water have (or SHOULD have) anti-siphon protection.
Waste water from your dishwasher drains to a sewer system. If water fills the drain hose completely, with no place for air to enter the drain, it IS possible for effluent to siphon from the sewer back into your dishwasher. Yuck, right? Doesn't happen often, but it HAS happened.
To prevent this, your dishwasher has an anti-siphon device called an AIR GAP, installed in the drain hose.
It is required by law in most installations. It prevents accidental backflow (siphoning) into the dishwasher from the house drain lines. A typical air gap re-directs water 180 degrees, and thus it has constrictions that can easily trap a chunk of food trying to pass through it.
Symptoms are the same as for any other blockage of the drain line, except that you may also see water flowing out of the air gap vents directly onto the countertop or into the sink.
Fortunately, they are pretty easy to open and clean. In most installations, it is a little chrome or brass blob with a couple of vent holes in it, sitting right next to your sink faucet handles. If it's not there, find the hose that drains your dishwasher into the sink trap or garbage disposal, and trace it back directly to the air gap.
Usually all that's involved in cleaning it is to pull off the little chrome blob and unscrew the top of the air gap itself. Both drain pipes will be exposed. Often you will find a seed or broken glass, or other bits of food wedged in there.
If the air gap isn't clogged, then it might be where the drain hose enters the house's sewer system. Disconnect the hose to the drain or garbage disposal and root around in there with a screwdriver to see if the drain is clear. If you've just recently installed a new garbage disposal, make sure the knockout is knocked out.