Wash it just like you would if the tail were attached to the horse- get it wet, and then use a shampoo (Quick Silver is fine- just don't leave it on too long, or your fake tail will get that lovely purple hue). Follow up with a conditioner, spray with show sheen and CAREFULLY brush out the tangles- just like you would with an actual tail or your own hair, from the bottom up, in small sections.
Hang to dry (not in the sun). If the ends are still really dirty you can have another go with the QuicSilver.
White/grey tails are very delicate and also very expensive (and you probably already know the latter....) so treat it well and it should last you a long time