Shelf liner that is torn or stained should be removed and replaced. To get it up, try using a hair dryer to soften the adhesive and make the liner more pliable. This works especially well for contact paper shelf liner.
Once you peel up all of the shelf liner, you're likely to have at least a few spots of adhesive stuck to your kitchen cabinet. Use a product like Goo Gone to get the last bits of your adhesive up off of the cabinets. Wiped down the interior cabinets with a mild dish soap. Rinse with another cleaning cloth, and dry with one last cloth. Now you're ready to place new shelf liner and replace the contents of the cabinet.