It is very hard to tell nowadays, where you can rack up kills on tight maps like NukeTown by using Hardline and getting a mass destruction weapon like the Gunship or the Chopper Gunner.
Speed hacks (he moves much faster than anyone ever can) and health cheats (he just does not die) are more obvious, so I am not going to mention them
Wall hacking is the most commonly used type of cheat where one can see through walls and track enemies from very far distances.
Some indications are: He has a ridiculously high kill-death-ratio.
Especially when deaths are less than five.
He plays with a sniper rifle the whole time, and can kill from the other end of the map before you see him.
He is prematurely firing before you actually show yourself around corners.
Shoots through walls/doors where you know
it's impossible to detect you there.
There are some caveats to the last one, though.
He might know you're there because:
There is a spy plane in the air and you don't have Ghost.
There is an SR71 in the air (Ghost Pro won't protect you here).
He has a motion sensor installed in your proximity
(Ghost Pro won't protect you here, either.
Only Hacker Pro makes you invisible to motion sensors).
He has previously thrown in a nade (flash/nade) and saw it "connected" someone
and he tried his chance by spraying in the possible places (it's obvious a lot of people camp the wooden rooms and the caravan wagon on the map Firing Range)
He has Ninja Pro and heard your footsteps from further away.
He is on a lucky day.
There is one test to almost exactly tell if he can see through walls: the step-ahead-step-back technique, in which you need to know the place the player in question is before hand.
As you are coming out of a closed space or round a corner, just run to the corner and before you really show yourself, back up a step.
If he fired before you appeared chances are high he was tracking you through the walls.
As you can see, finding out whether someone is cheating is not an easy task.
He might just be a good player, having a strong intuition or excellent knowledge of the map, and a good timing.
I would really not take this as a rule set to say yes or no, but as a checklist of questions you ask yourself before accusing someone.
For sake of completeness, check out Toastandjam18's interesting answer below about boosting.
gaming.stackexchange.com/users/4182/DrFish
Some clear indicators are: On kill cam he "jumps" from target to target always aiming to the exact same part of the body.
(The majority of the time being the head.)
He automatically shoots in predictive manner or immediately after aiming.
What must not be confused as cheating:
Randomly shooting at common camping places.
(Pros can also headshot)
gaming.stackexchange.com/users/5492/Fabián Heredia Montiel
Could you use the theater mode to replay the game from their perspective?
This may make cheating more apparent and would provide you with evidence.
The only caveat would be I'm not sure how accurately theater mode reproduces the game given players experiencing various degrees of lag from the server/host.
gaming.stackexchange.com/users/1169/Daniel Ballinger
There is also boosting in which the player uses a switch between his modem and PC/xpox/PS that cuts the connection long enough for him to jump places on map but not disconnect from the lobby.
This is easily seen on kill cam or in game.
Note that some people have a bad connection like when i played in iraq
but you can check that in the menu, if he is full strength then red barred then full strength again, then has
a high score chances are he/
she is boosting
gaming.stackexchange.com/users/11322/Toastandjam18
If you see someone aiming for a headshot through a wall, or surviving entire clips of ammunition or knifing, it's an indication of cheating.
gaming.stackexchange.com/users/21174/ricky watson
Another common thing I've seen is FALs shot in an extremely fast and predictive manner.
This means they are cheating by having a special controller that sends the fire button in repetition.
This is usually seen very easily in kill cams where even when starting and stopping firing, it is still being shot at a constant rate(rather
than like most people who gradually speed up and slow down)
gaming.stackexchange.com/users/138/Earlz
One I have noticed, though it may just be a bug in the game itself, is when you get them in your sights and your gun automatically "shifts" away from that player.
I thought I was going nuts, but one day I had put my controller down for a sec to grab the phone, and some geezer ran through my crosshairs and pushed it without me touching the controller.
This theory was proven fact when I followed him, tried to get a bead on him
and I couldn't.
gaming.stackexchange.com/users/21600/Hooligan
I have played enough Black Ops to know.
These conditions indicate cheating: Your opponent's gun shoots in the opposite direction from where he is aiming When you are unable to shoot until they kill you When they have care packages at the beginning of the game before they even have kills When your bullets are moved to either side of the player
When you empty your gun on them right in front of you, and they wait until you are finished and shoot you dead with one shot.
I have also heard a few dumb players brag about their cheating while playing the game.
There are players who are very very good who do not cheat.
gaming.stackexchange.com/users/12113/LeRoy Coffie
I've played games with some friends and they claimed that so-and-so was cheating.  I honestly just thought that he was a really good player.  What are some indications that someone is actually cheating?
How do I determine if someone is cheating in Call of Duty: Black Ops?
gaming.stackexchange.com
<call-of-duty-black-ops><cheats>
gaming.stackexchange.com/questions/12534
gaming.stackexchange.com/users/2986/Robb
It is hard to tell. Look for a ridiculously high kill ratio, playing with a sniper rifle the whole time and prematurely firing. Shooting through doors/walls is also a sign. While it is quite hard to tell nowadays, there are some indications. First and foremost, they have an expremely high kill-death ratio, or they play with a sniper rifle all the time, shooting before they even see you. They can shoot through walls and doors and their aim is not smooth while the bullets go in different direction from the barrel. The extremely obvious one is also that they refuse to die.
User suggests it is very difficult to tell. Most other users however are sure that there are clear indications.