Flip the chair over onto its back. You should be able to see the bottom of the chair. Remove the clip and washer holding the tube in place by using a screwdriver for additional leverage. Set the clip and washer aside.
Remove the old pneumatic cylinder from the base of the chair (it will just slide out) and examine it. Make sure it is identical to the replacement cylinder you will be installing.
Put the new cylinder into the base of the chair, pushing it in so it's situated the same way the old one was. Put the washer and clip back in place to hold the cylinder in. Flip the chair back over and adjust it using the knob. A few adjustments and sitting in the chair once or twice will be enough to tighten up the new cylinder and settle it in.