I have very thick, very dry, frizzy hair and a dry scalp.
I've experimented with various routines and feel what works best is a once a week washing of my hair (which I've always done anyway), with conditioner for dry/damaged hair/leave-in deep conditioner on the lower three quarters of my hair, leave for 5 mins, rinse with lukewarm water and done (no shampoo) - this seems to help with the incredibly dry, feeling. My hair is so thick that it doesn't get greasy very easily (only on day 5 or 6 post-wash usually)
If I use shampoo (even the ones without sulfates, made specifically for dry hair), it just dries my hair out a lot.