The beautiful thing about Halo is that there has never been a true skill cap. There's always room for improvement in many aspects of the game.
I've been playing since Halo 2 and I played competitively in Halo 3. I kind of skipped Reach because, in my opinion, it was a bad Halo game. But I digress.
You can use the same techniques I used and many others used in previous Halo titles to get better. Some techniques yield better results than others but the top two I would recommend are playing against players that are much better than you and practicing one play style or strategy or whatever it is you would like to practice over and over and over again.
The biggest thing that helped me in Halo 2 / 3 was playing with others that were way better than me. As long as your mechanics aren't awful, you will eventually pick up on the techniques and catch up to speed with the players you're playing with. This first suggestion works on your abilities and focus within your mind. Your brain will subconsciously adapt to the adjustments necessary to compete against the players who would normally beat you. This could take months but with enough dedicated time you'll eventually find yourself at the same level with the people you're playing against.
The second suggestion is to help you on your mechanics. This is the part of Halo that the skill cap is nearly infinite. Practice grenade placement. Practice subconsciously surveying every detail on the radar. Be aware of potential enemy positioning at any second of the match. Be aware of the lines of sight you are exposed to, and be aware of the routes your opponents will likely take to the center of attention. Practice subconsciously strafing / jumping in gunfights. Practice your aim. Make the CONSCIOUS decision MID FIGHT to let your DMR breath in between shots -- ESPECIALLY after taking two or more shots. All of these things add up to getting the edge over your opponent.
Practice DOES make perfect. It's all about baby steps.
Edit: The suggestions I made are proven to work in my own experience even up to a professional level. In Halo 3 matchmaking, I had a legitimate 50 in TS, a legitimate 45 in MLG, etc. I played professionals on many occasions and also competed in GB / MLG placement matches at high level play. If you'd truly like to get better, I highly suggest taking into account my suggestions above. I'm not kidding you, they do work.