A housemate of mine disassembled a "disposable" pepper grinder bought from Costco, but could not figure out how to put it back together after refilling it with peppercorns, so they asked me to do it.
Note: Before you disassemble your own grinder, consider searching for "refilling Kirkland pepper grinder." Most of the videos online show an easier, although slower method for doing just that. This method is faster, but has a greater chance of breaking the device.
Step 1: Make Sure You Have the Right Pieces for the Job
The parts above are arranged in the order that you put them on the grinder, with the bottom piece (thin ring) being the first. You may also want to grab a hammer or mallet, as you will need it soon.
Step 2: Place the First Three Pieces on Top of the Grinder
The thin ring, the cylinder, and the grinding mechanism should all fit snugly together, although the grinding piece won't want to go all the way into the neck of the grinder.
Step 3: Hammer the Grinding Mechanism Into the Neck of the Grinder
You will want to do this on a solid surface, like a workbench or concrete floor. Make sure that the metal bolt on the grinding mechanism is sticking upwards, as that is what you want to hit. This is the trickiest part of the process, so be don't be upset if you don't get it on the first try. You will be tempted to gently tap it in, though what it really needs is one solid stroke with the hammer to pop the grinding mechanism in!
In the picture above, I popped in the thicker black ring after the grinding mechanism went all the way in.
Step 4: Add the Cap to Check Your Work
If the cap fits snugly on the top, then you did it! Go ahead and grind your pepper. If not, go grab your mallet and try to hammer it again, without the cap of course.