Okay, first of all get Xbox Live. Then go into ranked matches, there you play people of your skill level and you get better. And also do campaign on Hard and/or Legendary difficulty.
Here are some helpful tips on getting better at Halo 3.
When using a rocket launcher, aim at you targets feet. This will inflict splash damage. Also aim where you target is going to be, rather then where they are.
If your target is around a corner try and throw a grenade at a wall so it rebounds near your target this will lower their shield and make killing them easier. Also use sticky grenade and throw them directly at your target because if a sticky grenade sticks onto a target its 1 Hit K.O. sticky grenades are Plasma and Spike grenades.
When up close to a target melee them while they're shield is down. This will guarantee a kill. Melee is by default on your controller, B.
When using a Battle Rifle aim for your targets head. This will inflict maximum damage to your opponent. When using and assault rifle, plasma rifle, SMG, Spikers or Needlers aim for your targets body rather than they're head because it is not guaranteed to hit.
When using a battle rifle 3 shots to the body is a kill.
Also when using a plasma pistol try to dual wield (use two weapons at a time) with a normal pistol as well. This is because when you charge up a plasma pistol to the max and fire it at a target it takes down the shield, then shoot with your normal pistol. This is guaranteed to kill your target.
Try to get into the habit of reloading regally so that when you do come in contact with an enemy you dont have to reload because you become completely vulnerable.
When using a sniper rifle try to Snope you target (no scope head shot). Although this is a technique used by only the most skillful snipers getting into the habit will be very useful when you are under attack by several enemies. Also dont stay in the same sniping spot the whole time because there is a smoke trail and they will find you.
You may not know this but when you crouch or stand right up against a wall you are not visible on enemy radars. This is useful when you are being a sniper or if you are going to assassinate a person (go up behind an enemy and melee them on the back, its 1 Hit K.O).
When you are being shot at and you dont know where they are or they are not visible when you look around they are either snipers, or they're invisible or they are crouching/against a wall. When this occurs you should never stop moving, just keep looking for them and jump jump jump and keep moving left and right up and down. This will make it difficult for you enemy to aim at you and get a good shot at you head.
Always look around you even behind you for an enemy. Remember you want to see them before they see you.
Never stop moving, nothing is harder to hit than a moving target. And when you are under fire, strafe left and right and mix it up a bit, and make your movements unpredictable.
If they're is anything other that you dont think that i have covered or i have not explained clearly, please e-mail me.
Also watch video's on Youtube because they often have video's with professionals playing against each other. You can learn alot from watching them. Type in Tsquared Halo 3 tips.
You can also Google Tips on playing Halo 3.
And practice practice practice