Take the piece of furniture that needs casters to be attached. Place it in a way that you can see and access the point where you have to attach new casters.
Using a large flathead screwdriver, remove the old casters from the bottom of the furniture. You can do it by putting the screwdriver between the base of the old caster and the base of the furniture where caster is attached. Now twist the screw driver, which will loosen the grip of the caster.
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Now you can use your both hands to remove the old caster from the furniture. Then clean out any dust or other particles on the base of the furniture.
Visit a nearby office furniture supply store and buy a set of casters to be attached. Make sure you buy the same, or a similar set of casters. If the casters are not exactly same in design, make sure their base is equal to the diameter of the old caster. It will allow you to attach the new casters easily, without any problem. Otherwise, you may have to visit the store once again, if the new one does not fit on your furniture.
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Now drill, if needed, in the bottom of the furniture, where you will inset the shaft of the caster. Make sure the hole is a bit tighter than the circumference of the shaft.