Get a friend. Have your friend sacrifice himself until the room is clear.
Always use a good combination of weapons, and think about your surroundings and enemies when choosing weapons. The sniper rifle is great until you reach the Flood. A good combination is the shotgun (the human pistol before you reach the Flood), an automatic weapon, and grenades. If you do not prefer to follow this example, then remember to use a combination of short and long range weapons.
Conserve ammunition. Never waste ammunition, always gather as much ammunition as possible, reload your weapon during any break in the action, and switch off any plasma weapon for a better one whenever possible.
Take it slow. Do not burst in to take all of the fire. Also, use the scenery as a cover. If you can fit behind it, you can hide behind it.
Use the enemies themselves to your advantage. Remember that each enemy type has their own mannerisms and characteristics.
Take shortcuts when possible. Here are some examples. In The Silent Cartographer level head directly to the security override station. In the Assault On The Control Room level, after you get one of the early Banshees, in the area after you go under the tunnel you cannot take the tank through, the double bridge will be directly above you. Ride the Banshee to the bridge and skip a large portion of that level. Taking this shortcut means there will be no more enemies throughout the rest of the level. In the 343 Guilty Spark level, go to the secret area with the 2-D trees and follow the cliff through the structure that goes indoors. In The Maw level, after the dropship gets taken down, you will keep going. Continue until you see the first open door on your right. Enter there and take another right. This can shave a good minute and a half off the time it takes to get to the Longsword at the end of the level.