I rinse the piece well with a pressure nozzle attached to the garden hose. I leave it out in the sun for a day or so to kill any bacteria (not likely), then I put the piece into the tank. Local rocks will work well to weigh the piece down. If it leaches tannic acid, I just change out the tank water every few days until the water clears. The amber color doesn't affect anything and will go away in time.
"Fear not, my young apprentice. Just change the tank water."