Place your tail in the sink or tub (depending on how big it is, and whatever is most convenient). Fill the sink or tub and toss your tail in. Saturate it only with COLD water. Its very very important to only use cold water when washing fake fur. Heat changes the texture of your fur, which is not something you want.

          Once your tail is saturated squeeze it along its length to loosen any dirt which may have become trapped in the fur.

          Next, use a mild clean-rinsing detergent, such as Woolite.. though it won't hurt to use regular liquid laundry detergent if that's all you have, as long as it doesn't contain bleach. Don't use powders, since they will just get trapped in your fur if they don't dissolve all the way. Gently rub and squish your tail along its length, especially in the areas which you think are soiled.

          Once you've soaped your tail up to your satisfaction, rinse it until you don't see any more soap bubbles. Squeeze it along its length and try to get most of the water out, don't wring it, though, that may stress the seams or kink the hairs.

          Shake your tail out, this will get a little more of the water out and fluff the fur up. Then hang your tail up somewhere to dry, it might take a while depending on how thick it is. You can come back every so often and squeeze the water out of the tip. Once your tail is mostly dry, you can comb it out. Don't put your tail in the dryer, dryers produce heat and can ruin the fur on your tail! Also, don't use a hairdryer, unless it has a cold-air setting.