I understand the benefits of tannin...but I admit that I can't stand looking at stained water. I use leaf litter in some tanks, and collect my own driftwood, so it's an ongoing compromise.
The "fastest" way to get rid of tannins? Just don't add wood, leaves or other sources of the stuff! Carbon works to remove it if you simply must have it gone immediately...
But the "best" way is, IMHO, a normal regimen of large, frequent water changes. Tannins, nitrate, hormones...water changes remove them all.
I have exactly one piece of "purchased" driftwood, a nice chunk of Mopani that I received as a gift. It's been in my Musk Turtle's tank for several years now. That tank gets a 100% water change at least weekly, so the wood has been in something like 150+ complete changes of water and still leaches tannins to a visible extent. My wife, who dotes on the turtle, complains so much about the "pee" in the water that she will do water changes on that tank for me (which involve simply opening and closing valves). That, to me...is the best thing about tannins!