Nine times out of ten, a dishwasher that fills with dirty water isn't a broken pump or a bad valve. It's the air gap on top of the counter, next to the faucet — that little chrome cylinder most people don't know is part of the dishwasher system.
The air gap is designed to keep sink water from siphoning back into the dishwasher. When it clogs (usually with food debris that made it past the filter), water backs up. Pop the chrome cap off, pull the inner plastic cap, and clean out whatever's in there. Reassemble. Run a cycle. Fixed.
If the backup continues after cleaning the air gap, the next suspect is the drain hose from the dishwasher to the disposal. Then the disposal itself. Then the branch drain. If you've cleared all of those and it's still backing up, call us.