Turn one of the dining room chairs onto its side so that you can easily access the wheels.
Place one drop of a lubricating oil into the area where the wheel attaches to the leg. Allow it to sit for five to 10 seconds and then grasp the wheel with your hand. Pull the wheel away from the chair leg using firm force until it comes loose.
Wipe the oil off of the wheel stem with a paper towel. Measure the depth and width of the metal stem with a tape measure to determine the size of the new wheels to buy.
Place the metal stem of a new wheel into the hole in the bottom of the dining room chair leg. Push it upward as far as it will go until it snaps into place. Hit the wheel with a rubber mallet to help push it into place, if necessary.
Repeat the process to replace all of the remaining wheels on the dining room chairs.