Cannons occur when three or more balls end up in contact, at least one of which is a yard-line ball.  Unless one is a yard-line ball then the Laws (Law 19b) do not allow the orientation of the balls in contact to be changed. Typically cannons occur if one ball is rushed behind a yard-line ball or at the start of a turn when three balls are in contact.

In a full cannon, in the same stroke as a croquet is played on the centre ball (Yellow in the examples below), a roquet is made on the forward ball (Blue). Hence it is croquet and roquet in a single stroke.  The striker then picks up his ball and takes croquet from the forward ball.  The advantage is that all the balls are moved off the boundary.  Note that the croqueted ball (Yellow) may not leave the lawn, but the others may.

The diagrams below detail recipes for setting up cannons.  Depending on how the balls are struck (e.g. sharply or with follow through) the outcome of the stroke will change.  Therefore it is essential to practice the strokes.

Note: 1.25" is 32 mm and 1" is 25.4 mm or the diameter of a 2p coin