Turn a hair dryer to the highest heat setting. Direct the heat to one of the corners of the shelf paper to soften the adhesive.
Grab the corner of the paper and pull it off the shelf slowly to prevent tearing it. Continue directing the heat onto the paper as you pull it back until you remove it completely. If you have difficulty removing the shelf paper, use a putty knife to help release it from the wood.
Remove any remaining pieces of the shelf paper with a putty knife. Use the hair dryer to loosen the pieces the best you can until you remove all the shelf paper.
Apply a commercial adhesive remover to the shelf to remove the sticky residue left behind. If you do not have access to an adhesive remover, apply vegetable oil to the wood and rub on it with a washcloth.
Wash the shelves with warm, soapy water after you remove the adhesive. Rinse the wood shelves and dry them completely before painting or applying new contact paper.