The Pistol. The Pistol is one of the most useful weapons in the game. All-around powerful, with a good balance of range and damage. Excellent in almost all situations at all ranges. Go for headshots; it three shots to the head on normal settings will full health and shields, and roughly six body shots. Try keeping your aiming reticule at head level. The 2x zoom is another advantage, but this means you want to try to keep a longer range on other players. The true beauty of the pistol is pistol-sniping, or using the pistol as a sniper rifle. You can get off more shots and it's stealthier, too. The pistol is full-auto, but firing one shot at a time is far more accurate, especially at range, so squeeze the trigger for each shot. The melee is slow, but ammo is plentiful, so rarely will you find yourself forced to use it.

The Sniper Rifle. Arguably the best sniper rifle in any game ever. Take your time and go for headshots. You only have 4 shots in a clip, and reload is slow, so use your shots wisely. Ammo can be scarce, another reason to be cautious. Also, the sniper rifle has nasty contrails that instantly give away your location if you miss. When sniping a moving target, drop your crosshairs somewhere in the projected path of their head and fire when it turns red; this tactic is called "leading the target". 
The sniper scope can be an all-consuming little world of its own, especially when zoomed in all the way. Look at your motion trackers and keep moving. Never strike from the exact same spot twice; you will be found eventually. In case you are rushed, a shotgun is a very useful thing to have along with the sniper rifle. 
The rifle is also a valuable spotting tool that you can use to the advantage of your team, reporting enemy movement and being aware of approaching threats. Keep in mind that if you fire, you may give away a good position; a pair of snipers is often useful, one for spotting and one for interdiction of targets. Move laterally when trying to frustrate a sniper's efforts; jumping just makes you a better target. Counter-sniping is rarely a wise thing to try unless they have expended their clip and are reloading when you hit them.

The Shotgun. The shotgun is an elegantly brutal weapon. It is best at close range, when a single blast can penetrate shields and kill instantly. Headshots, as with any weapon, are most powerful if you can't get close enough to blast them at one-hit-kill range. A useful tactic is vehicle-hunting: toss a plasma grenade onto a vehicle, and when the occupants scramble out to avoid it, blast them with the shotgun. Keep a long-range weapon with the sniper rifle; the pistol is good to weaken them up and then finish them with the shotgun.

The Assault Rifle. The AR is a fairly weak weapon. It's best for medium range; it is too inaccurate for long-range (burst fire helps) and the shotgun is better at close range. It's best in tandem with a plasma pistol-- take out their shields and gun them down. Melee is fairly good, which makes it a decent close-range weapon, but still not as good as the shotgun. Full-auto fire is the only thing that makes it really useful.

The Plasma Pistol. It may seem like it sucks, and it can be frustrating when it's all you have. But the Plasma Pistol is actually a good weapon-- in the hands of a truly skilled player. It will fire as fast as you can pull the trigger, which makes it a good suppression-fire weapon if you can flip the trigger fast. Shooting enemies in the back is damaging and useful, and any shot will stun them, making their motion and aiming sluggish-- try it against a large vehicle. It also has a very useful overcharge feature that will drop shields no matter what strength they are at-- even if the enemy has an overshield. Overcharged bolts home in on moving targets, but don't rely on the homing too heavily, and it doesn't home in on vehicles. Melee is incredibly fast as well. Best to keep in tandem with an assault rifle or pistol; take out shields and finish them off.

The Plasma Rifle. The plasma rifle is a well-rounded weapon with good automatic fire. Each burst is less powerful than a single hit from a plas pistol, but still powerful, especially against shields. Stun factor is also a big help. Head shots do twice as much damage after the shields are down. Watch the heat meter; it takes a long time to cool off and that pause is often enough to be fatal. The fast melee makes it good for run n' gun tactics. Overall, the plasma rifle is a good weapon to keep with any other weapon.

The Rocket Launcher. The SPNKr is one of the most powerful weapons in the game, with excellent direct damage and good splash. Hitting directly in the torso is not advisable, because it makes it easy to miss if they dodge slightly; aim between their knees and their feet. Jumping is a good tactic, as it gives you a better firing angle to hit their lower legs with; in general, the higher the ground you control, the better. The projectile is slow, so lead your target; it takes time to get a feel for the speed of the rocket. The launcher is useful in Oddball or CTF for blasting the skull or flag away from an enemy about to seize it. If you miss a shot, switch weapons and finish them with something else. The last shot is for emergencies, and you probably won't get the time to fire a second shot if you wait between shots or for the horrendous reload. Watch the target distance, as you can easily kill yourself, too. Meleeing is slow, so don't bother unless the target has his back to you.

The Fuel Rod Gun (computer versions only). The fuel rod launcher is extremely powerful-- even overbearingly so. It takes three or four shots to kill (two extremely accurate ones), but the fuel rod gun features the semi-automatic abilities of the plasma pistol. You can fire as fast as you can click. The rods are launched in an arc-- kind of like a grenade, the only indirect fire weapon in the game with the exception of the grenades. Remember to keep away from your target far enough that you don't get taken out yourself. Also, the fuel rod's melee is almost as fast the plasma pistol's. This is a hard one to defeat and if you see someone with a fuel rod gun it is best to either stay away completely and snipe them (rifle or pistol) or charge them so that they take themselves out when they kill you.

The Flamethrower (computer versions only). The Flamethrower is an excellent close-range weapon, and can be used in situations that a shotgun would also work in. It takes a few seconds (maybe 2 or 3) of direct exposure to kill with the flamethrower, but it keeps burning after you turn off the flame, so if you can get their shields down and take a chunk out of their health they're pretty much dead. Watch for lighting yourself on fire-- you will if you're too close. If someone is rushing you with the flamer, back off and take them on with a pistol, AR or other medium range weapon.

The Needler. The Needler is amusing, and perhaps one of the most humiliating kills. But it's not really a very powerful weapon. It's great if they can't dodge. The homing projectiles are slow, but if you can pack a bunch of them into him you will take him out. The melee is horrendous, so don't bother, and definitely pack something short-range. Ladders, walkways and other tight spaces are the best locations to find good targets for Needlers.

The Fragmentation Grenade. The frag grenade has a short fuse, which makes it good for popping off quick blasts at an advancing or retreating enemy. Toss one as the enemy is coming around a corner. Good for ambushes, and they're harder to see than the plasma grenade. Throw one as you're about to die, and sometimes you will kill someone in the blast. The suicide grenade becomes a reflex.

The Plasma Grenade. The Covenant grenades are sticky, meaning they bond to targets, and deadly if you can stick one. They have a longer fuse, so they're less useful if you can't stick them, and they have a tendency to hook to the left when you throw them, so bear that in mind. Accuracy is important. Plas grenades don't bounce, so toss them into a corner where an enemy will soon be without worrying about it hitting you. Good against vehicles; toss one on a Ghost or Warthog, then finish off the passenger(s) with a shotgun as they hop out.

The Melee Attack. Using your gun as a blunt club, or melee attacking, is useful when you are out of ammo or are at extremely close range. It can be fun and humiliating. The rate at which you can melee varies with each weapon, but the damage is the same. Plasma pistols and assault rifles have among the best speeds. Hitting someone on the back is an instant kill, so if you're ambushing someone with a cloak, get behind them. Running give you 50% extra damage, and landing on them from a jump gives 75% extra, so keep that in mind when you can't get in back of them. Both the skull from Oddball and the flag are melee weapons, so use them for extra humiliation.