Know the layout of the map and where the power weapons are.
Get good with the power weapons. And if you suck with them, don't take them unless your giving them to you teammate or so no one else gets them.
Aim for the head, should be common sense.
Use the Battle Rifle, its becoming more common, but most people don't pick it up, take it. Its range will come in handy.
Use grenades all the time. If your losing a fight, throw a grenade, could put you back in the fight or score a point. Or nothing and you die like you would have before.
Also use motion radar. That should be second nature.
When someone is coming through a doorway and your hiding behind it, throw a grenade at the door, if done properly it will take their shields out, leaving you for an easy kill. Or jump when they are coming through, you will have seemed to disappear and take the advantage.
Spartan Laser has a scope, use it.
Take cover when you have to, if your losing a fight, you can run to regain shields, however, depending on where you are that is a bad idea, and the opponent is also regaining shields.
Sniper is just about the best weapon, BR is, but if you can get no scopes down as well as head shots, you will own almost any match.
Mostly pretty basic stuff right here. You really just need to play and figure out a style.