Lay out some newspapers or a drop-cloth to prevent any grease from getting on your floor. Office chair bases contain a gas cylinder that is lubricated with grease, and it can get messy.
Turn the chair upside-down so the the center of the base is visible and accessible. Laying the chair with the back touching the floor is an easy way to perform this task.
Locate the holding clip in the center of the base. Remove this with needlenose pliers or a flathead screwdriver. Slightly bend the clip open, and slide it off of the piston.
Remove the washer on top of the base around the piston. This will simply pull off.
Pull out the base by pulling and turning counter-clockwise simultaneously. The base and gas cylinder should pull out as one piece, with the gas cylinder hidden inside. Watch out for the grease coating the base. Replace the new base and reverse the steps to install it.