It is quite difficult to find paid internships, but there are some.
Most of them are in art museums, however. Two contacts: Office of Museum
Programs, A & I Bldg. 2235, Smithsonian I., Washington, D.C. 20560.
For internships specifically for conservation, contact the American
Institute for Conservation, 1400 16th St. N.W., Washington, D.C. 20006.
 
There is a listing of internships in MUSEUM STUDIES INTERNATIONAL, the latest
edition being 1988, with a new one coming out sometime this year. A local
museum or your library may have a copy. Or visit the Museum Reference
Center...same address as OMP. You can also ask if AAM has a new listing
of any kind....1225 Eye St. N.W. #200, Washington, D.C. 20005. Good Luck!