This question can be difficult to answer due to the wide range of materials and the unique nature of handmade artifacts. Many good publications and references are available on the general care and storage of art objects. One excellent series, offered by the American Institute for Conservation (AIC), is available here: Caring For Your Treasures.
Because no two works of art are alike in age, condition or meaning, a decision on how to repair or restore an artwork should only be made after careful evaluation by a trained professional. The American Institute for Conservation offers a referral system that can help you find a qualified conservator in your area here: How to Choose a Conservator.
Conservation training in the United States typically combines graduate-level academic study and years of hands-on training in museum or private conservation laboratories. A few universities offer advanced degrees in art conservation, while smaller private programs are available in some specialized areas. You can learn more about the requirements and curricula here: Become a Conservator.