Weeding Through the Weeds
One of my local streams just had a bunch of water dumped into it from an upstream dam. This washed a lot of weeds and other debris into the river. If making it to another river just isn't an option here are a few things to do to save the day under these circumstances.
Abandon dry flies and go to bright nymphs - If water is high and there is a lot of debris it is likely that fish will not be looking up to feed. However, it also means that a lot of drifting food is present so fish could still really be feeding well. The classic fly for this situation is the San Juan Worm. Use bright colors like pink and red if the water is a little off color. More subdued colors work when the water is relatively clear. Fish deep and slow. Also try various bright bead head nymphs like Rainbow Warriors, Copper Johns, and Lightning Bugs. You will have to clean them off regularly, it stinks to do but it needs to happen.
Go big - Debris filled water or dirty water makes fish much less wary. Go up a few sizes with the flies you fish and feel free to go up a size or two in tippet since visibility is likely poor. You may be surprised at how large a fly you can actually catch fish with in these situations. I've seen size 10 and 8 flies catch fish in rivers where 18s were the norm.
Fish near shorelines - Often when flows go up fish move to the calmer waters right against the shoreline. I have caught fish in these situations by short line nymphing just inches off of the bank. Be methodical and work every pocket since in dirty water it may take a few more drifts before you get your fly squarely into the fish's feeding zone.
Fish side channels and tribs - If you know of or can find smaller tributary streams or side channels fish these well. Side channels or small braids sometimes don't get quite the volume of drifting debris that the main channel will have and fish often move into tributaries or hang right at their mouths to avoid hard currents and poor visibility.
Hopefully your rivers stay clear but if you find yourself on debris filled water don't give up and you may just catch the biggest fish in the stream.