General rules I follow, and I usually get a high if not top spot in games are:
1. Radar! I know so many fools who don't check their radar that get my knife in their back. You want to become good at using peripheral vision to notice your radar, especially during firefights.
2. Awareness! Awareness is an extension of radar, but it's far more important. Your radar only measures so far away, distances which don't cover long or most medium ranges. Awareness is even more important in games without radar, so you need to constantly look around, and listen. The game has a number of audio cues that indicate someone is approaching, be it steps or hard breathing in the case of sprinters.
3. Fight on your terms! Don't go rushing into a battle you aren't likely to win, especially if it's in the open. More often than not, they've got a teammate that will help them out at range, a teammate you probably don't even know is there until you notice the damage on your screen. Another aspect of fighting on your terms is that you can lure your enemy to where you have the advantage, especially in close quarters if you have a closer-range weapon. Typically, any enemy which sees you, in most game types, is going to proceed to hunt you down. Many of these enemies are fools and will saunter around a corner, only to receive a shotgun to the body and a melee.
4. Know your enemy! Learn the different weapons of the game, understand the different armor abilities. If you see your enemy has a shotgun, do everything within your power to avoid close range combat, because you will die very quickly. If your enemy is sniping, attempt to engage in close range combat. If you catch a sniper off guard, typically they're going to fire their full clip of 4 rounds almost randomly, and cause little to no damage to you. Even if you don't kill them, and they get you, you've caused them to lose an entire clip, which can yield 4 kills instead of 1 kill if they're good, at a loss of 3 kills. As another note, Elites and Spartans often have different available powers, and different starting equipment, it is important to know both.
5. Know your power! Understand that every armor ability is not useful in every situation. Active Camo won't do anything to help you if you've already been spotted in the open and are being shot at, but it's jammer ability is very useful, especially for organized assaults, even if you don't slow down and make use of the actual camo. Evasion can easily, easily get you killed by flying off the map if you're not careful. Armor Lock takes a good deal of experience to master, and it definitely isn't often useful. Sprinting is usually a good all-around power, but it won't always save you. Jet packs are useful but you're a sitting duck once your enemy realizes you can only fly(and jet packs are extremely easy to see due to their bulky backpack effect on Spartans). Drop shields are extremely useful in tight situations, able to heal teammates' and your health, while temporarily shielding from damage. Holograms are iffy, and easy to identify, I don't recommend them except for say Snipers game types.
7. Trickery is encouraged! Elude and deceive your enemy whenever possible. Similar to fighting on your terms, feigning a retreat can draw an enemy forward to release a plasma grenade to the body. Creativity is encouraged. A few days ago, I used my active camo ability to jam the radars of three pursuing enemies while I ran up a tower. I then jumped down, assassinated one, and blew the other two away, all the while I hearing their yells over the close-coms.
8. Communicate, dammit! Don't be shot at and not tell your teammates where it's coming from. If you don't tell your team a sniper is across the map, they're usually too dumb to see the "x has sniped y" or to look around, giving the sniper a few free kills. Make that sniper work for his kills, dammit. There have been far too many times where I have, as the sniper, simply annihilated a team because they wouldn't communicate where I was, until I simply ran out of ammo. On another communication point, if you're close enough to your enemy, they will hear you speaking. Shut your mouth unless you want them to know you're there. One another aspect of this is not to blow your teammate's cover. I have many a time been patiently sneaking up on an enemy sniper or team, and some fool idiot goes running by and alerts them to our presence by appearing on their radar.
These are the only ones I can think of at the moment. Most of it common sense, some of it is learned through experience, all of it means knowledge is power.