Shanghai's quick and efficient subway system—called the Shanghai metro—is an excellent way to get around town, and the network is growing exponentially every year. English maps and exit signs abound, and the single-ticket machines have an English option, too. In-car announcements for each station are given in both Chinese and English. Keep your ticket handy: you'll need to insert it into a second turnstile as you exit at your destination.
Transport cards costing Y30 are available from metro stations. Add as much money as you like, and use them to pay for taxi, metro, ferry, and bus rides. The transport cards aren't discounted, but they'll save you time you would have spent joining queues and fumbling for cash. To purchase, say, Wo yao yi zhang ka (which means "I want a card").