Moving your office furniture is much easier if you can break down the pieces and store them in boxes. While there are many different kinds of office chairs, most have a similar mechanism that can be disassembled.
Lay your chair on the side and inspect the wheels. Many wheels have a clip that hold them onto the chair base. Push the clip to release the wheel stems and remove the wheels. If there is no clip on the stem, pull the wheels out of the base, tapping the top of them with a rubber mallet, if needed, to loosen the stems.
Unscrew the screws at the side of the chair that hold the arms to the seat. Most chairs use Phillips-head screws, but some may have hex screws, which require using an Allen wrench instead of a screwdriver.
Place the chair upside down on a table to access the base and lifting mechanism. Pull up on the chair legs to remove the mechanism post. This may come off easily with some chairs, but with others the post may be stuck. Hammer the seat bottom around the post with a rubber mallet to help loosen it while pulling up on the legs.
Spray lubricant around the post of the chair if it is still stuck in the chair. Allow the lubricant to work for 10 minutes, then try again to remove the post. It should come right off.
Tap the end of the post sticking out of the middle of the chair legs. This should pop the mechanism from the leg base and remove it from the chair.
Pack all screws together into a zip-top bag so they don't get lost.