Do not rinse out the conditioner from your hair
Instead, go ahead and apply some of the moisturizing shampoo all over your hair, remembering to not forcefully scrub your head. Make sure that all of your hair strands are facing downward. Next, thoroughly rinse your hair until all of the water runs completely clear. Squeeze out any excess water before applying a deep conditioner from mid-length to the ends of your weave itself. Leave this in for around ten minutes before rinsing with warm water. Pat your hair dry with a clean towel.
These are steps that also work for curly and wavy hairstyles as well, though more conditioning may be required.