Six-card Stud is really nothing out of the ordinary as far as game-play goes. Plays the same as 7-card Stud, with the only difference that players get one card less dealt (that will usually be the last face-up card).
There are a couple of variations to Six Card Stud, one called "Alligator Stud”, which is meant to make the game play better at NL and PL. In Alligator Stud, the game begins with each player receiving one face card and one hole card, followed by a betting round, then two upcards, then another up-card, and finally another one. Obviously, there are betting rounds in between these deals.
The other variant is Zanetti Stud. In this game, the initial deal consists of an up-card and two downcards, with players being restricted to using only one of their down-cards in their final hand.