In American Rules, a major step between beginners and intermediate players is the ability to attack. Even at the top level, there are players making mistakes as to how and when to attack. Here is a somewhat lengthy guide to the whole concept. Check out the croquet glossary if any terms confuse you.
An attack is when a player (we'll call her, the striker) roquets a ball in an attempt to go to other balls rather than going to the striker's hoop. Many goals and strategic priorities may be satisfied with a well executed attack including making the very wicket she seems to be avoiding. As with most tactics, timing is everything. Towards the end of the game, an attack may be defensive or solely a means for running down the clock. In most circumstances, however, the striker has offense in mind when attacking.
In the best attacks, the striker makes her hoop on the current turn. This opportunity is ripe when the opponent leaves a ball or two near the striker's wicket or both balls joined close enough to ensure a rush (more on that later) and near by the striker's hoop so as to minimize the risk of missing the wicket (while three ball dead). Occasionally the opponents are between the striker's current and next hoops. In this case she can rush to the pioneer hoop, take off to the other balls, and manufacture a rush to her wicket to earn a quick 3-ball break, with the fourth ball ready for an easy pick up.
Most attacks are meant to set up the partner ball. These plays cater to proficient break runners because often the striker ball finishes the turn three ball dead. The only justification for such a risky play is the partner making a handful of hoops and possible leaving the striker in position at (if not peeling her through) her hoop.
Setting up the partner ball is an art in and of itself, but the basic concept is to leave partner with a ball close enough to hit (a rush is better, and liveness is paramount) and a ball at his hoop (or pioneer hoop if deadness or location is an issue). The last component of any good set up is nullifying the danger ball. The danger ball, or hot ball, is the next ball to play. If the danger ball has deadness, the striker can get crafty but often the best bet is to isolate the hot ball, leaving it far from any hit in chances.
The key to easy attacks is to begin with a rush. If the striker can get close to the other balls, the more opportunities she has. Depending on the difficulty of the court or the needs of the partner ball, the striker may roll both balls close to the target balls or just take off. Frequently, the striker should hit the spent ball (that just played) and put it close to partner while trying to get a rush (on the danger ball) towards the striker's hoop. If partner is not close to the opponents, it may be wise to either hit the spent ball and send it away (to partner or his hoop) or hit the danger ball, get a rush on the spent ball to the striker's wicket or a location that helps partner.
Ther is more than one way to skin a cat, but the important part is to accomplish the goals in question with very little risk. If it is possible to end the attack with a big croquet shot towards position at the wicket. Every so often the striker may end up with an wasy hoop shot or a shot that, if missed, will end in a position that helps partner (his current or next hoop) without helping the danger ball.
There are always confounding factors in an attack, but the differences make the game that much more interesting. Sometimes the striker must take off to the attack, or roll close to a boundary ball from great distances. Whatever the case she must know the goals, the risks, and the contingency plans. There is always another option, but if she finds the correct play, she must not be afraid to put on the blinders, keep her head down and execute.