There's a very specific answer to this, and it's that you should use the Dyson Airwrap when your hair is nearly dry. Fully wet hair can be too heavy to easily wrap around the barrel, so using the Coanda drying attachment to take out some of that moisture is a good idea before you start drying.
With that said, using hair that's too dry will mean that it's not easily styled, because it's already set into its normal shape. If you're starting with fully dry hair, we recommend using a spray bottle to spritz a little water through your hair so you've got something to work with.