The best way to get around Shanghai is to use public transportation.  The city's systems are very well integrated.  One way to reduce the the time it takes to buy individual tickets, figuring out each individual fare, and the amount of cash you carry on hand is to purchase a Shanghai Public Transportation Card (Jiao Tong Ka).  The card can be picked up subway station ticket information booths, and it works on a debit system.  You put money on the card, and the balance is reduced as you use the card.  The best feature of this card is that it can be used for all modes of in-city transportation: bus, subway, light rail, taxi, and ferry. You can add money to the card at many convenient stores (they will have the same logo as is on the card in the window if they do), the subway station, and at McDonald's throughout the city.

 The "Bible" for information about the SPTC and the subway system is located at:  http://www.exploreshanghai.com/metro/

To get a jiao tong card you go to the service center in any metro station and simply say "yi zhang jiao tong ka" ("one traffic card") and give any amount, remembering 20 yuan is the deposit.  The staff will remind you in broken English  that there will be a deposit of 20 RMB for the card. You just smile and nod and they will give you the card ready for use. Maximum value which can be stored on the card is around 2000 RMB.  You can watch your balance each time you exit a station.  The turnstyle machine will show you the remaing balance. You can add money to your SPTC at special automated kiosks before you go thorugh a station's turnstyles.  If you only have 1 RMB left on the card you can still ride the metro but you then have a minus on it when you exit a station so the gate will not let you pass. In this case you just approach a metro staff at the destination and hand over your card together with cash. They will NOT top it up but just collect the balance. For topping up you must proceed to the service center of the station. To use the card in the taxi it is recommended to tell the driver "yong ka" ("use card") or show it to him before he stops as they usually take it for granted that you pay cash. Note that you can not use your card anymore once the driver flipped the meter at your destination - so you want to tell him well in advance! 

Ferries run between Pudong and Puxi.The ferry costs between 2.5 and 5RMB ($0.40 and $0.80).The ferry runs until 9:30PM and is a great way to see the night skyline. You may want to make other arrangements, though, if you're on the other side of the city.

Buses run all over the city and a transportation card is helpful because they don't make change. Bus stops are named by road, or sometimes by an interesting site, or by an intersection name.

The subway has fewer stops, and it is easy to learn what parts of the city can be reached.  The Di Tie (subway) and Qing Gui (light rail) use the same transfers and you can get tickets from machines in the stations. There are "touch" screen ticket If there is an English indicator on the machine, you can get instructions in English. The machines take bills and coins and give change.

Be aware that the train fills up and that you may have to "push"  to get in and out of the train - especially at peak time.