I used to play chess through school and college (and occasionally at uni) and was considered one of the best in the school (I even participated in a national tournament once - but got knocked out at my second game). It got to the point that I didn't play much because by mutual agreement I stopped playing with the only other person on my level (not boasting, that's just how it was, I could even beat computers sometimes) as we never finished any game... unless I played utterly recklessly and confused him completely (or lost by being too reckless). In the end I started passing my time teaching others.
What Hath says above isn't far off. However...
People try to control the board with pawn formations. This can work, but it limits your options as well and if one goes down the whole formation collapses soon afterwards, usually leaving you exposed. It is also obvious where the danger areas are and so easy for your opponent to avoid. It is much more satisfying to swoop down from the opposite side of the board with a bishop.
Have a plan, but be prepared to adapt it, and as Hath says make sure your plan can have multiple outcomes. If your plan revolves around getting a queen on to the back line and suddenly it is no longer viable, know what you are going to do instead.
Remember the objective.The aim of the game is to checkmate, you don't have to remove every enemy piece to do this. Also, you don't have to retain all of your pieces to do this.
Learn how to sacrifice. I don't mean play recklessly, but sometimes it is worth trading a piece to take something nasty off the board, clear space, or manipulate the opponent into a sequence of events that is advantageous to you.
The queen isn't the most important piece on the board. It is the most powerful, certainly, but it is just another tool. You don't have to use your queen and don't be afraid to sacrifice your queen if it serves a legitimate purpose. Some players will fixate on their opponents queen, this can make it useful as a distraction from your real intent. Some players will defend their queen at all costs and become blinded to the fact that they are being out maneuvred because the queen is continuously being put under threat (reacting instead of being proactive).
Learn to use knights effectively. Starter players typically like to play around with knights but struggle to use them and then ignore them in favour of more conventional pieces. Experienced players later go back to them and can do wonderful things with knights. Everybody likes to get a queen onto the opponents back line, but you can cause just as much havoc if you can get a knight in there - just be prepared to lose it as it has short range and can't escape when trapped. Knights are also very good for board control, they are hard to predict and players sometimes have difficulty visualising where they can hit.
Castles (or Rooks) are your tanks, or bulldozers. They are easy to predict, easy to visualise. You are rarely going to surprise anyone with a castle move. They are your blunt instrument to make a killing blow or to lock down a row. Because of their movement they can be quite vulnerable and it is easy to trap a castle out of position. But, because they are easy to understand, people keep a weary eye out on them and this can again be used to your advantage.
My first Windows PC (Win95, 1GB HDD, 16MB RAM
) had a chess program on it which I discovered had a built in "cheat" function. This worked by showing me what the computer was "thinking". It showed all possible combinations of moves of how the computer thought the game was going to turn out and the assigned probability of them, and then the computer made its move accordingly.
BUT, while the computer can come up with all of these combinations, it still could only make one move each turn. The way to beat it was to consistently make sure that it always made the wrong move by not doing what it thought you were going to do (but not doing stupid things, you still needed a strategy to win). This holds with playing against people. You can strategise all you like but each round you can only make one move, so you need to keep as many options open as possible wherever you can.
