There are three main parts:

1) The latch body (or cylinder). The lock barrel goes in one end, and there's an opening in one side. There's a small black plastic tab that slides into the opening, which the lock barrel will move outwards to lock the latch mechanism. Make sure that part is in place when you finally assemble it (it can be inserted with the tumbler in the locked position, and is held in when the tumbler is in the unlocked position). Opposite this opening there's a lug that limits the rotation of the cylinder once it's in the housing.

2) lock barrel, with six tumblers protruding. The last tumbler of the lock is what keeps the barrel in the latch body. Through wear (this tumbler is also what limits the key motion when you lock and unlock the mechanism) there may be a slight burr on the edges that makes it a bit sticky to push in for removing the barrel. The barrel goes into the latch body with the retaining tumbler showing through the latch tab opening . You will have to wiggle the tumbler a bit, maybe push in the last element with something small, etc., in order to assemble it. Note: it is possible to assemble it in the locked position as well as the unlocked position. If locked, though, you can simply pull out the black plastic tab to prevent locking action, if you want, and you can probably reach the last tumbler to let you withdraw the barrel again.

3) The housing. If you look in, there are two slots in the inner diameter. One is slightly wider; this is where the metal lug on the cylinder goes. The plastic latch tab extends into the smaller of the two to lock the latch. You can insert the cylinder into the housing with its lug in either slot, but in one of them there will be more rotation. That will be the correct one.

Once these parts are assembled, you just bolt on the arm to hold it together. One of the engagement holes is larger so it will only go together one way.