American pattern files have two different types of cut:
Single Cut: Used with light pressure for smooth finishes and to sharpen tool cutting surfaces. A single set of parallel teeth runs diagonally across the width of the file.
Double Cut: Used with heavier pressure than single-cut style for faster, rougher-finish cutting and more rapid material removal. Diagonal rows of teeth run across the width of the file in opposite directions.

Different cuts may be present on the different surfaces of the same file (i.e. a flat file with double cut on both sides, and single cut on both edges).

They also come in several different coarseness of cut:
Bastard: Heavy removal with coarse finish.
Second: Light removal with fair finish.
Smooth: Finer finishing than second cut.

These are the patterns:

Some advice Alan L. posted on a forum:

“…yes there are better files! Get yourself a Nicholson Magicut in the largest size you can find, which I think is about 14 inches. A long-angle lathe file is nice too. A big honkin' file really cuts down on the amount of work you have to do. Follow that file with a smaller single-cut mill bastard or mill smooth used in a drawfiling motion, which means hold it at about 90 degrees to the work with the handle in your left hand and the tip in your right as the blade points at you, and pull straight towards yourself. As Mike F. noted about, this cleans up the deep scratches and flattens the surface.

As Redwulf noted, use soapstone or chalk rubbed into the file to keep it from getting little bits of steel caught in the teeth, since that causes BIG deep ugly scratches. I usually clean the file every few strokes with a small wire brush or by tapping the end on the floor to clear the filings.”

“Note to those unfamiliar with files: They come in different grades of fineness. We're all familiar with the "mill bastard" file. "Mill" is the shape, and the degree of tooth size and spacing goes as follows: Coarse, Bastard, Smooth, Dead Smooth, and Fine. Bastard and Coarse come in double-cut or single-cut, referring to the way the teeth are cut. If they're an X-pattern, it's double cut, which cuts faster but leaves a rougher finish than single cut.”