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Purchase a kit labelled for your lock's brand. Remove the exterior door knob. Pop the the cylinder out of the back of the knob. Remove the cylinder retainer ring. Slide the cylinder plug out of the cylinder housing. Remove the old pins from the cylinder plug. Insert the new pins to match the code in the instructions. Reassemble the lock.
There are re-keying kits that contain all the tools you'll need available for most lock brands. One brand's kit usually doesn't work for others, so check your lock's brand and purchase a kit that matches it. You can find kits online and at hardware and home improvement shops. Read your kit's instructions carefully, in case there are any minor differences specific to your brand. The kit will provide a thin, wire-like tool that you can use to remove the knobs. Insert your key into the lock and turn it to unlock the door. Slide the wire tool into the small hole on the side of the interior door knob. This releases the knobs and will allow you to pull the outside knob out of the lock. You can also use a stretched out paperclip or pin instead of the tool. If you've lost your key, you'll need to remove the entire lock and bring it to a hardware store or locksmith to have a new key made. If your lock doesn't have a side poke hole, you're better off replacing the whole lock. Your lock is probably complicated enough that it requires a locksmith to rekey. Once you've removed the exterior lock face, look inside the knob and check for any sheets of plastic or metal that hold the lock cylinder in place. Slide them out if any are present, then put pressure on the key, which is still inserted into the keyhole, to pop out the lock cylinder from the back of the knob. If your see rust or other signs of wear and tear inside the lock, you should just replace the entire lock. Your kit will come with a wrench-like tool that you'll use to remove the retainer ring that secures the cylinder housing. Slide the tool around the horseshoe-shaped ring, then turn the tool to pop off the ring. Your kit will come with a cylinder follower, or a tube-shaped tool, that you can use to slide the plug out of the housing. Push it through the cylinder housing from the side opposite the keyhole to pop out the plug. Keep constant pressure on the plug and follower, and make sure they're always in contact as you slide the plug out, so that the lock pins and springs don't pop out and fly everywhere. On some locks, you can just turn the plug over to empty out the old pins. Other locks might require you to pluck them out with a set of tiny tweezers supplied in the kit. Check your kit's instructions to find out exactly how you should remove your plug's old pins. Once you've removed the old lock pins, slide the new key (provided in the kit) into the keyhole. The new kit will come with colored or numbered pins, and its instructions will include a code. Use the kit's tweezers to insert the pins into the plug's slots so they match the code. For example, the code might list the correct order as blue, red, red, blue, yellow, starting from the side opposite the keyhole. Correctly installed pins should be flush with the surface of the plug; they shouldn't stick out over their slots. Once the pins are installed, push the plug back into the cylinder housing. Slide the retainer ring back into place, pop the cylinder back into the door knob, and replace any plastic or metal sheets that secured the cylinder. Push the exterior door back into its slot in the lock, and rotate the key until it the knob pops and locks into place.