After a 3C preemptive opening, a 3D bid asks for a THREE card major.
This means that 
  (1) Responder bids 3D with a five card major
  (2) Responder bids 3M with a SIX card or longer major

From "Preempts A to Z," the responses to 3C-3D are
  3M   three of the OTHER major
  3NT  no three card major
  4D   both three card majors

From "Bridge: The Bidder's Game," the responses to 3C-3D are
  3M   three card major
  3NT  no three card major

Furthermore, after 3C-3M, opener rebids
  3NT  shortness in the major
  4C   doubleton honor support
  4x   three card trump support, shortness in the bid suit
  4M   doubleton support (less than Jx)