As the most powerful of the pieces and therefore the most valuable, the queen has the difficult combination of being the ideal attacker, while also being vulnerable to attack by the enemy. New players are often divided into two camps on how to use the queen; some novices are so enamoured by the queen's power and mobility, that they use their queen almost to the exclusion of the other pieces, while others are so afraid of losing the queen that they keep her locked away safe from harm and miss out on the opportunity of using their most powerful piece. Of course, the ideal approach is somewhere in between.
The queen is best suited to a role in attacking the enemy. Her ability to strike out along ranks, files and diagonals gives her an unparalleled ability to create multiple threats at once and overload enemy defences singlehanded. Here is an example of the queen's awesome attacking power:
The presence of the queen makes any attack much more dangerous, and while the enemy queen is still on the board, the king must huddle in fear behind his defensive pawns. Because of this, one way to fend off an attack by the opponent is to try and exchange queens.
Because the queen is so valuable, she does not make a good defensive piece. Because of the queen's value, simply being protected by another piece is often not enough - when attacked by an enemy piece of lesser value (and aside from the enemy queen they are all of lesser value) she is usually compelled to move and abandon whatever defensive duties she was performing.
Many players are afraid of their opponent's queen, and try to exchange queens at the earliest opportunity. This really isn't necessary (unless you love endgames, at least), as the queen is often vulnerable to attack if brought out too soon. An attack on the queen is almost like a check, because the opponent will almost always have to save their queen. You can often use an attack on an exposed queen to gain time to move your piece to a better square. Here is an example: