Clubs are an apparatus given to the older gymnast, as it requires that the gymnast must be as dextrous with the left hand as with the right as there are 2 clubs, though I do like the younger gymnasts to have a go, so they are more prepared when the time comes.
Swings, circles, mills and throw/catching are the fundamental elements of this apparatus, rolling and tapping add to the musicality of a routine.
Swings and big circles can be executed in the wheel plane or frontal, the clubs act as an extension of the arms, performed correctly give a very streamlined elegant look. Small circles or mills are a little harder to master; this involves a pivot action of the head of the club between the thumb and first finger, not the circling of the wrists. Working A-symmetrically is another skill to be mastered and is very effective, as one arm and club swings around in a full circle in the wheel plane (side) the other works the club works in small circles/mills in the table plane.
You can purchase junior clubs that are half the size of senior clubs to help the younger gymnast acquire some handling of clubs, but they are advised for the more advanced gymnast.