Learn The Maps
The number one advantage veteran Halo 3 players have over beginners is knowledge of their surroundings. If you take the time to learn the maps by choosing local play (as in playing offline by yourself or with friends) and explore the weapon and power-up spawns as well as the teleport and possible sniper locations, you'll have a leg up or at least an even shot against the competition.
Adjust Your Look Sensitivity
To adjust your look sensitivity, press "Start" at any time during matchmaking and click the directional pad once to the right. From there, press A to enter game controls. Within game controls, scroll down one space to "Look Sensitivity" and click "A." Now you can bring it all the way up to 10 (insanely sensitive) for ultimate mobility and turning, but very difficult aiming or 1 (very low sensitivity), which allows ultimate aiming capability but almost zero movement in close quarters. If you're a sniper/ battle rifle player, you might want to keep things on the low end. If you like to dual wield a lot or use the shotgun, try something a bit higher. Four is generally a good choice, but try different sensitivities and see which works best.
Movement and Shooting
To truly master Halo 3, you'll have to learn to shoot on the run as well as strafe. Shooting on the run comes with practice, but never stand still while you're shooting unless you're sniping...you're too easy a target. Instead, hold the right analog up and the left analog to the right or left---this will help you strafe. Try jumping while shooting; this will confuse less skilled players and give you a decided advantage from the beginning of the fight. Finally, if there's one weapon to master, it's the battle rifle. Practice your aim with the battle rifle and make sure you can zoom in (click in right analog) and get that head shot when your enemy's shield is down.