My washer was making a loud rhythmic click/thunk sound during the agitation cycle only, everything else functioned normally.
I disconnected all electric/water hookups and took the washer to a more open area. I tipped it over so it was laying on the back, this way the motor was oriented "upwards" from the central agitator and the motor's weight would be supported during work. Before I took everything out I was able to see the drive coupling from the side and slowly rotate it, and it was obviously broken into two pieces.
First I removed the metal clasps holding the plastic reservoir against the motor; they were not screwed in so they simply had to be snapped off at the top and maneuvered out of the oblong holes in the motor casing. Then I removed the two similar, but longer, clasps which held the motor onto a metal plate by a similar design. These longer clasps required removing a screw from the top of each clasp (which held the clasps onto the motor casing). After this, the motor required a bit of lifting to take off the plate but there were no other screws or attachments. With the motor set aside, I unscrewed the two bolts holding the plate against the agitator, and the broken coupling was easily removed.
After that all I had to do was place the new coupling and put everything back the way I found it. I would recommend having some WD-40 for the new couplings because they have the reinforced metal in the center; it's nice and strong but it definitely made it a tighter fit especially with the agitator shaft. Overall it took me a while because I'd never done it before and I was figuring it out as I went. But for anyone with experience with tools or similar machines it wouldn't take very long I'd imagine.