Rule 6-12.a (in part) ... The player of the attacking team in the attacking
half of the rink whall place the stick within the white area first. ...
No other players shall be allowed to have the skates (on or off the ice)
inside the face-off circle or beyond the parallel face-off lines extended
or come within 15 feet (4.57 m) of the players facing off the puck. ...
 
This last sentence has been quite vigorously enforced starting with the
92-93 season - on the first offense (for a given face-off) the offending
team(s) must replace the face-off person, second offense causes a minor
penalty.  One of the best changes that was made last year, in my opinion.
 
Thanks for the question - I've been meaning to refresh my memory about
which stick goes first for some time, but hadn't gotten around to it.