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Step 1: Remove the MASTER LINK!
Now, locate the master link in the chain. There should be a link, with a clip on it, like the one in the picture. I generally move the chain so that the master link is on the UPPER portion of the chain. By that, I mean, The chain loops around the 2 sprockets. 1 on top, and one on bottom. If the master link is on the upper portion, the open part of the clip should be on the right. When you reassemble the chain, be sure to put the clip (Which we will now remove) back on this way. Kapish?
Once you've located and positioned the master link, take a pair of pliers, or channel locks, or needle nose pliers, and unclip the clip. I put 1 jaw of the pliers on the pin that the clip is snapped around, and the other jaw on the open portion of the clip. It should unclip relatively easily...
Once the clip has been removed from the first pin, it's pretty easy to wiggle it off. Do that. You will now see an oval link underneath where the clip was. This will also wiggle off. Do that.
At this point, the 2 pins of the master link are exposed. Simply undo and remove the master link.
Step 2: Break That Bad Chain!
So, screw down the bigger screwy thing onto the chain, snug. Then turn in the knob to start pushing in the pin. You'll want to put a wrench on the knob, or a screwdriver through the knob. I usually turn in 9 complete turns for a 415 chain.
After that, back up the knob 10 or 11 turns. Then unscrew the other part. You should be able to remove the chain breaker at this point.
You will see that the chain link pin is ALMOST completely out from the link, but not entirely. This is the preferred way to open the chain, because if you need to put the chain back together, the pin can be pushed back in fairly easily. If the pin comes all the way out, good luck trying to put it back in. Not fun.
At this point, just wiggle the loose link from side to side until it comes off.
Put the master link back on (in reverse order from taking it off) and Cha-BAMMM! Chain has been shortened.