Basically, fill up a sink or a bucket with lukewarm water, add whatever shampoo you've got lying around (don't use too much) and work your fingers around the wig and through its fibers gently. You can add some conditioner if you like, in my experience it helps prevent tangles. Rinse it, and dry up the excess water with a towel. Let it dry out, maybe put it near a fan so it doesn't mildew. (This happened to me once, it was a pain!) Or, if the wig is heat resistant, you can use a blow dryer to dry it. Then you're done!
EDIT: Forgot to mention, if the wig is long, use the tub since it's got more room.
Otakuthon 2015 cosplay: Mairu Orihara, Junko Enoshima, Komari Kamikita