TL:DR - Spectate them. That's the easiest way to know for sure if someone is cheating or not. A lot of servers have spectator slots enabled but you need to be whitelisted to access them. Joining their discord is usually the easiest way to get whitelisted. It's also the easiest way to get someone banned if you can record them cheating, obviously.

If you want to be able to gauge if they are cheating or not from playing against them you need to have put the hours in. Being able to spot inconsistencies of what is possible, what is lucky and what is fishy.

Wallhacks are the hardest to find the inconsistencies with, imo. There are so many ways for a good player to know where you are in this game. Everything from audio (footsteps, suppressed gunfire, throwing out medpacks/ammo/grenades) will let a person know where you are even if you don't show up on the minimap. But you can sometimes tell if the person is fishy by the way they move after they've killed.
Like is the person a 1.2 kd schmuck that can barely move yet he always peaks you perfectly? Maybe it's worth throwing out an in-game report and see if any admins are willing to spectate him for a little bit.

Seeing as most hacks have a spectator warning (I assume most have that at this point) he'll either turn off his cheats and if he does and he starts playing worse you can get a personal confirmation that he is maybe not legit. He might also just leave the server, which is another personal confirmation that he isn't legit... Or maybe he just got lucky a few times and at worst you wasted some admins time.

Being able to gauge if the person is aimbotting revolves around being able to feel how quickly you usually die in an engagement and from what gun. How many times did he hit you? Did he miss any of the shots he took at you? Did he get in a headshot or two that made it feel even quicker? Does it happen every time you go up against this player at any distances? Is it a lowlevel player or is it a rank 140 who have spent the last decade playing this game?

Aimbot *can* be very easy to tell. Are they ragehacking? Beaming people across the map and killing everything in ways that just doesn't seem possible even from the best players you've come across? He might be cheating.
Is he melting you in 3 shots yet never kills you with headshots? He might have his aimbot set to 2headshots, 1 bodyshot to throw some people off from the fact that he is cheating.
Maybe he is just killing you with 2 shots. At that point it might be a damage modifier but I haven't personally come across too many of those. At least I haven't noticed it.
Now if the person uses no recoil/no spread and the person have good movement and awareness in the game it would be hard to tell if he was cheating without actually spectating him. 

So lets say I've found a person that is fishy and I want to check their stats I usually start with their level followed by their k/d and accuracy of their top guns (that aren't snipers, dmrs, shotguns or pistols) A lot of the time they have shit (or average, depends on how you see it) accuracy. 12-14%
I follow this up by creating a snapshot to refresh their stats. Is their newer guns higher accuracy? What do their battlereport history look like? Did they go from never being able 1.2kd to suddenly dropping 3kd+ rounds? Are their headshot ratio off (If they aren't using a sniper)? Lets say 40% and up with assault rifles across a 30+ kills or so. 
(It's very much worth noting that an abnormally low hs/r is weird too. There is no way in hell you wouldn't land a single headshot across a few different matches in this game.)
At this point if I think it's justified i'll throw up a report on BF4DB. Sometimes I'm wrong and it gets closed. Sometimes there isn't enough to warrant a bann but it is fishy enough to keep the report open. Sometimes they get banned.

What i'm trying to say with all this, except that im tremendously bored, is you need the gamesens to be able to tell if someone is fishy or not. This comes from playing. A lot of people will throw out hackusations left and right without having any idea of what's going on meanwhile real hackers don't even pop up on these guys radar because they aren't flashy.

Dudes cheating. 

o7, thanks!

How do one check for them? How does it work? 

Maybe you're just shit mate