Place the chair backside down, in such a way that the wheels get off from the floor and you can see them properly.
Take a large screwdriver and insert it between the base of the bottom of the chair leg and the base of the caster. Twist the screw driver, as it will loosen the grip of the caster from the bottom of the chair leg.
Image Courtesy: la.wikipedia.org
Now hold the leg of the chair firmly with one hand and pull the caster out of it by using your other hand. In some cases, the casters are screwed in the leg. In such case, you can unscrew them from the leg.
After you have the caster in your hand, take it to a nearby office furniture supply store and buy a complete set of casters. Make sure you compare the new casters with the old one. The new ones must be same in size and diameter of the old ones. At least, you must match the base of the new casters with the old one.
Image Courtesy: ontimesupplies.com
Now slide the new casters in the leg of the chair. Usually, they easily slide into the hole in the bottom of the leg. If that does not happen, you can smack it by using your hands.