Turn the chair over so that the bottom of the seat is facing up. Prop the chair against a desk or table to make it easier to work on.
Find the bolts and screws that hold the seat to the frame of the chair. Every chair model is slightly different, so you will need to look closely to find all of the fasteners.
Remove each screw and bolt from the chair seat assembly. Have a cup or small container ready to hold those screws and bolts as you remove them.
You will need to have them on hand when you reassemble the chair.
Lift the seat off the chair frame and set it aside. Be ready to catch any small pieces that come off.
Place those pieces with the screws and bolts.
Hold the hydraulic cylinder under the seat and place a pipe wrench on it. Turn the pipe wrench until the cylinder loosens, then pull the cylinder out.
Slide the new hydraulic cylinder inside, then reassemble the chair.