Shag is a couple's dance. The basic step is a six (sometimes eight) count and involves a simple forward-and-back motion and a change step at the end; with the six count, this consists of two triple steps, followed by a rock step for the ladies and an optional kick-ball for the gents. Men lead with their left, naturally, and women with their right; standard swing turns are often used to break the pattern up, but the shag is mainly about footwork. "Mirror moves," or moves where one partner mimics the other at the same time, as if they were reflections of each other, are also popular. Advanced steps include the Round House, the Boogie Walk, and the Roll Out. You can, however, acquit yourself well with just the simple basic step.
(NOTE: Carolina Shag, which is what most folks are referring to when they mention shag dancing, should not be confused with St. Louis Shag, an older and different dance.)