SAFETY FIRST: Protective gloves and eyewear are recommended at this point.
Place the motorcycle on a stand.
Remove the rear brake master cylinder reservoir cover using a #3 Phillips head screwdriver.
Remove the two bolts holding the metal reservoir cap guard in place using a 10 mm wrench.
Remove the master cylinder reservoir cover and rubber diaphragm. Clean and inspect the rubber diaphragm for tears or other damage. Replace as necessary. Fill the reservoir with DOT 4 brake fluid from a tightly sealed container.
Pull off the rubber cap over the bleeder valve and crack open the bleeder valve on the brake caliper using a 10 mm wrench. The photo is not of the Kawasaki KLR650 caliper but the procedure is the same. This valve is usually very tight so use a 6 point box end wrench or a 6 point socket and ratchet to prevent rounding off the head. Snug the bleeder valve down.
Place a length of 6 mm inside diameter hose on the bleeder valve and place the other end in a container.
Pump the rear brake pedal several times and hold the pedal down. While holding the pedal down, crack open the bleeder valve. The rear brake pedal will travel all the way down and brake fluid and/or air will come out of the bleeder valve. Tighten the bleeder valve before releasing the rear brake pedal. Pump the pedal several times again and repeat the process. Check the reservoir occasionally and add more brake fluid as necessary. Continue this process until clean brake fluid comes out of the bleeder valve and there are no air bubbles. The rear brake pedal should feel firm.
Add DOT 4 brake fluid to the reservoir until it is between the upper and lower lines.
Collapse the rubber diaphragm accordion. Place it on top of the reservoir and install the cap, tightening the cap securely.
Reassemble the motorcycle.