Summarize:

Your flamethrower does massive damage, but it's very short-ranged, so you must use it carefully. Don't charge at your opponents head-on while blasting your flamethrower. It's intimidating, but you'll probably be gunned down before you can even singe another player. Instead, try to sneak up behind a group of enemies, get up as close as you can, and then let your flamethrower rip! As a Pyro, fear is essentially your middle name. You generally live to cause chaos and confusion in other players. Apart from an oncoming Heavy, nothing is more intimidating to an enemy than a set of flames that continues to damage him or her after you are out of the way. As such, you'll find that players tend to scatter and run from you, which helps to keep the enemy team from executing cohesive strategies. As a Pyro, Spies fear you more than any other class. If you see the brief silhouette of a player flicker before you, immediately let loose with your flamethrower to reveal any cloaked Spies near you. Even spies in disguises can be set on fire by a vigilant pyro, instantly blowing their cover. The Pyro is the only class that can effectively break an ubercharge. You can use the flamethrower's compression blast to separate a medic from his uber-ed companion. If you separate the two by enough distance, the medic will no longer be able to share his uber with his buddy and your teammates will be able to gang up to finish both off. Do this when the uber players don't see you coming, as an uber-ed Heavy will make short work of an oncoming Pyro.
Take your enemies by surprise. Disrupt the enemy team's coordination. Reveal spies with your flamethrower. Use the compression blast to break ubercharges.