Each hairpiece, long or short should be detangled before washing. Short hairpieces - just run a brush through. For longer hairpieces: take bunches of hairs, hold halfway along their length and brush away from the roots towards the ends. Work up each bunch until you get to the roots.
Waves and curls need more attention. Take small sections and from ends to root, brush or comb, gently winding each curl around your finger - this avoids pulling out the curls.
If you have makeup on the inside of the hairpiece, rub a little neat shampoo into this to remove all traces of grease