The others are right, but there are a few key elements to gaining skill. Some naturally have it, some get it through practice. Here's some tips.
1: Know your map. This means weapon/vehicle placements, pathways, and frequent battlegrounds. Take a look at some of the heatmaps to see where the action is at.
2: Know your weapons. Get used to the guns you use, and how you use them. Learn the strong and weak points of every weapon, and where they spawn on the map. Try to "feel" the range and ammunition in the gun, just by using it freqently. Any weapon can be useful, so don't always go for power weapons (though they are helpful).
3: Play some other gamemodes in Halo 3. You could go in Forge to learn spawn placement, respawn times, and enemy spawn locations as well. Campaign is useful for training. Start out on Easy, then move to Normal. The Flood levels tend to improve accuracy and weapon usage, while fighting brutes is more like a player in matchmaking. If you have a friend/sibling, let them play some 1v1 splitscreen with you. Invite some more friends over and play 4 player splitscreen. As long as your friends aren't already pros, you should all be able to learn the ropes of the game at a steady pace.
4: Accuracy and strategy are essential. Find a control scheme that is right for you and practice with the thumbsticks. If you can achieve headshots, you're bound to win a lot of matches. You also want to plan out a strategy for maps, such as special routes that let you get behind your enemy. Another good part of strategy is teamwork. If your team can communicate, you're a TON more likely to win. Say Player A is killed at a power weapon spawn and the other team takes the weapon. He can tell you instead of the enemy popping up later to surprise you with his new fancy shotgun.
Good luck getting up the ranks.