Remove the stove's burners if they are removable.
Moisten a non-abrasive cleaning sponge with plain white vinegar and use the sponge to wipe down the stove. This will remove any dust, dirt or residue that might be dulling the appearance of the metal.
Fold a paper towel and drop two to three drops of baby oil onto the center of the folded towel.
Polish the stove by making small, circular motions with the oiled paper towel.
Wipe down the stove with a clean, dry lint-free cloth. This will remove excess oil and bring the stove to a shine.