That's the trick, clean as you go.
First thing I do when I'm done eating is wash the dishes I used.
Yep. I said it. It sucks.. anyone wanna invent a mobile dishwasher? Ha someone keep me company!
Washing the big dishes is fine. You can make big, circular scrubs and be in your own little mental space while you do it. Also, it's a good feeling to get those big ole' dishes out of the sink.
But the silverware. The god-damned silverware. I always wait till all my forks and knives are used up and dirty, then do them all at once. Takes forever and requires serious concentration.
Fuck silverware.