That being said, here are a few of the possibilities for the offense:
The “I” formation is very simple, and very common in football. The quarterback stands directly behind the center (known as being “under center”), and two running backs, the fullback (the one closer to the QB) and halfback, are lined up behind the quarterback (the first picture). As a variation, the fullback can be lined up slightly to one side of the “I” or the other (the second and third pictures).
A Pro Set formation looks very much like the “I”, but the running backs are on the same horizontal line (or “split”) behind the quarterback, instead of being in a vertical line behind him.
You don’t see this one in the pros very often, but the “T” is one of the older formations. The QB is under center again, but he has three running backs lined up in a row behind him, and two tight ends (or one wide receiver and a tight end), one on each end of the offensive line.
The Shotgun is used primarily in passing plays. Instead of being under center, the QB stands about five yards behind the center and will catch the ball in the air instead of being handed the ball by the center. This allows the quarterback to have a better view of the defense and his receivers as they proceed down the field. He also has a little more time to find an open receiver and throw the ball since there is a little more space between him and the rushing defensive lineman. The offense can arrange its receivers and running backs in a variety of ways, but there is usually a running back standing next to the QB. The running back can take a handoff from the QB and run with the ball, or he can be used as another blocker to protect the quarterback.
If the Shotgun and the “I” had a baby, it would look like the Pistol. Instead of standing five yards behind the center, the quarterback is a little closer, maybe three yards behind him. And instead of the running back standing next to the quarterback, he is behind him. The Pistol can be used in running plays or with the option, which is when the QB runs with the ball and either keeps it or pitches it back to a running back.
The Wishbone is a variation of the “T” and the basis for its name should be clear from the picture below. In this formation, the offense uses three running backs: a fullback who is standing directly behind the quarterback; and two halfbacks, who are split behind the fullback. This is usually used on running plays, with two tight ends in this formation as well, one on each end of the offensive line; there can also be one tight end and one wide receiver, or two wide receivers.