The Draw Offer
Nothing in chess has more psychological power than a draw offer. The draw offer can be a very good thing, saving time if it is obvious that nobody can make progress. However, I am under the belief that offering the draw hurts the player who offers the draw if the game continues.
I will give an example of what I am talking about. Let's say John is playing against a higher rated player. The game is a long and hard-fought struggle, but the game simplifies into a rook ending that is a theoretical draw. John would really like a draw against a higher rated player and is hoping that his opponent will smile, look up at him, and calmly shake his hand. But what if his opponent declines? Suddenly, John has to come back to the moment and find the best moves. He then plays moves that will limit his opponent's play to draw the position and forgets about any chances he may have. John's opponent has a great chance to win the position because he is higher rated and is likely to know the position better and the fact that John is now playing scared chess. This can happen many times at the club level, but can be prevented by just trying to find the best moves and waiting either for his opponent to offer the draw or letting the game draw naturally. The same goes true if your opponent offers a draw. If he offers a draw, he likely wants you to accept. Only an idiot would offer a draw that he doesn't want you to take. If you decline his offer and play a few more moves, your opponent will likely make an inaccuracy playing for a draw and you could sneak an extra half point out of the game.
In conclusion, it is best to rarely offer a draw and to decline your opponent's offer. Playing the game out will help you learn more about the great game of chess and can get you some much-needed points.