Master Chief’s Buttery Love

Learn the Maps, and the strategies used on them:
Every map is laid out in a specific fashion for a reason. Bungie has done a fairly decent job of keeping most of the maps balanced terrain and weapons wise. However this doesn't mean that there aren't certain strategies that should be employed for specific maps. One such strategy that I like to use when playing team slayer on Narrows is to focus all attention on the bridge and hold that. If you can find the focal point of each level and maintain a hold you should gain some advantage. Some maps have lifts that will fling you into the air, these provide excellent places to kill and be killed. Throw some grenades up the lift first to clear your way, then proceed up yourself. You can also use these to access high perches that are great for sniping.

Run Away:
Who said there was any shame in running away and living? On team games there is no reason for you to be the lone hero. Strategy and teamwork are very key, giving free kills to the other team as you charge all four of them alone doesn't help. If you find yourself being out numbered the best course of action is to duck and cover (run away) until you can have a team mate assist you. That does not mean you can't throw sticky grenades back at your enemy while running away though. Some of the best kills have been made with stickies thrown in desperation run away attempts. Besides, it looks cool to show your friends later.

Avoid Fighting in the Open:
A lot of the maps in Halo 3 are center specific, meaning they have a centralized kill zone. Gaurdian for example has three circular kill zones that are wide open. Typically these areas are fantastic bait for grenades and rockets. You should try and avoid running blindly through these places at all costs. On the other hand, if you can find a nice spot to sit and hurl large exploding objects at players that are careless enough to run or stand in the middle of these open spots, you should do so with zeal. You can rack up double and triple kill medals pretty easily if you get a well placed rocket into the middle of a team standing clumped together in these sections.