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Start with an assault rifle

The assault rifles typically have the best handling, best accuracy and cause the most damage. The downside is that the fire-rate is often lesser than some better SMGs (submachine gun). An SMG would also be a wise choice as a first gun, so whichever you unlock first, go with it and stick with it for a while. Purchase some attachments and get going!
Your first attachment should be something like red-dot-sight, as this can improve accuracy for you (although it doesnt improve accuracy of the weapon overall) and can make long-distance kills a lot easier. Attachments are very, very important, as they expand the efficiency of your weapon, which is particularly important when playing modes that allow for attachments and perks.

Always have a grenade ready

Never go into a match without at least a semtax (sticky grenade) or flashbang. The default smoke grenade is OK, but is better used for infiltration and team-based objectives that dictate moving into an enemy-filled areas; they act as great cover!
Unless you have the scavenger perk (which allows you to restock on ammo from dead enemies), use your grenades wisely, especially if youre planning to camp. If you have a general idea of the main spawn points of the enemy, get close enough and hit the area with a flashbang or concussion grenade to see if anyone is there. If you get a hit, throw in the semtax or frag grenade.

Use the Flak Jacket

Particularly useful on smaller maps, the Flak Jacket is great for avoiding damage from grenades and explosives. Explosions in Black Ops can be quite devastating and large, so this is very useful if you find yourself running into enemy grenades often.
Its also a great way to avoid death from claymore, as they can be hard to spot if placed well by the enemy.

Take advantage of the Decoy Grenade

The decoy grenade is fantastic for objective-based team-modes. If youre having trouble infiltrating a certain area, you can use this fantastic little piece of equipment to trick the enemy and surprise them while they look around for an enemy that doesnt exist.
If you can work together with a few teammates, this piece of equipment can be quite effective. Throw, flank and attack should be the order when using the decoy grenade, and while it can be effective when using it on your own, its particularly useful when you have people around you to back you up. Remember, not everyone in Black Ops runs to the sound of gunfire not everyone plays for the kill! Watch out for the enemy that hangs back.

For camping, use the motion sensor

If youre planning on sticking to one area, place the motion sensor near-by at a door entrance or at the top of a flight of stairs. Ensure you keep an eye on your map, as the sensor doesnt beep whenever an enemy is nearby like the heartbeat sensor in Modern Warfare 2.
The sensor only tracks maybe 10-20 meters out in a 360 degree space, but its enough to ensure youre safe in your area, especially if youre trying to hold a spot on the top floor of a building with only one entrance.

Use Combat Training

Combat training is surprisingly good and a fantastic way for newcomers to learn the ropes of the gameplay. If youre not particularly quick on the aim-down, head into Combat Training with a weapon of choice, as well as a few friends if you like.
The only downside is that anything you unlock and earn cant be carried over to online play. However, its still a great way to choose your loadout and get used to a weapon before heading online where it all matters.

The Theater is there for a reason

The theater is a great addition in Black Ops. It records your action over a number of days and allows you to go back and watch the action to see where you went right and wrong.
Its a fantastic tool to see the hotspots where everyone died during a match, and you can use it to familiarize yourself with the maps.

Move in and out of cover

Taking cover is actually integral to success in Black Ops. Youre going to get shot-down from behind quite often, so the best thing you can do is ensure you always have your back to cover, or are at least behind solid covering to protect you from enemy fire above.
Whenever youre moving around a corner, ensure the weapon crosshair is always in the middle of the screen, and jump straight into cover, even if for a split second. This way, if anybody is coming at you from the other direction, you have them in your line of sight while youre protected behind cover. Never run directly around a corner while sprinting.

Choose Killstreaks Wisely

While having air support is great early on, chances are that as a newcomer you wont be getting enough kills to call it in. Start off small with 3, 4 and 5 killstreak rewards, this way you can call them all in quick succession and more often. As you improve, bump the killstreaks up.