The basic pawn storm is one of the first long term ideas that I learned. Take this early position. White is finished his opening.
Rather then "looking for something to do," white starts a co-ordinated attack. This attack known as a pawn storm will involve, bringing both his rooks to g and h files, removing blacks dark square bishop to create a colour complex, and pushing his pawns in a charge on the king. It is this last point that defines this as a pawn storm.
Whites f3 knight and light square bishop are also available to jump into battle at a moments notice. If black is any good, white should be aware that black might try a long term plan of his own, in this case an attack on the center or a pawn storm of his own on queen side are likely.