After removing the debris, observe if the water flushing the small waste in the downspout is backing up than continuing to drain away. This will mean that your downspout is clogged and will require manual unblocking.
The way for using a pressure washer is to remove the debris found at the base of your downspout, and then put it in a trash bag. Then, direct a stream of water through the pressure washer, with a high GPM and through the downspout. When you find the water is running out freely from the downspouts, you can move on to the rest of the gutters.