As laowai88 says, take Line 4 to Dalian Road, use Exit 3, and walk three city blocks southwest and you will run into the prominent museum.
To get to the Metro station at Peoples Square, you walk less than two city blocks to the Peoples Square Metro station, Line 2. Take Line 2 eastbound, towards Pudong, four stops where you transfer at Century Blvd from Line 2 to Line 4 counterclockwise. Third station on Line 4 is Dalian Road. Quite simple, really. See www.exploreshanghai.com Fare is 3 yuan and probably faster than taxi. Taxi cost around 22-25 yuan or more, depending on traffic.