How to hit a cut?

They basically refer to it as a shot that moves from left to right.

There are two different ways to do this.

You can either hit a cut by opening your stance and opening the face a little at address a la Freddy Couples or you can set up with a square stance and cut across the ball with an out to in swing path a la Martin Kaymer.
 

or you can hit a knuckle fade.....but you better have a decent swing

..align your body to where you want the ball to start

..align the clubface between where you want the ball to start and the primary target, so the ball can land and run out to the primary target

..position the ball slightly forward

..and swing with an in to out swing

Depends on the fade, if i want to hit a low fade, i will play the ball back in my stance and cut across it. If i want to hit a high fade, i will play the ball way forward in my stance, like off the inside of my front foot for an iron, try to block the shot right, were i finish my hands higher, less around the body. I really like the 2nd option, i do that for drives i want to take about 20 yards off, and for irons that i want to land softly. 

Tom Watson refers to it as a "slice" in his Lessons of a Lifetime DVD.  He doesn't use draw either, but calls it a "hook".  They are all different terms for a shot that curves away from it's starting direction.  But as stated above technique can vary to create different height shots that curve in different directions and start out on different lines.

For me,

Fade = controlled

Slice = uncontrolled

That's is the difference, a fade will stay in your workable zone, while a slice will fly out of it. I know some people learn to play a slice, but it is unpredictable, i've seen many players play decent golf with a slice, i stand behind them, they aim the same amount ever teebox, and that ball would start at different angles, and slice different amounts, it was wild. 

Agree.  Also, fade means, "I meant to do it".  Slice is whoops!