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 amount of cash you carry on hand is to purchase a Transportation Card (Jiao Tong Ka).  The card can be picked up subway station ticket kiosks, 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.

Ferries run between Pudong and Puxi.  The Pudong pier is a short walk to all the major features of the skyline.  There are two piers from Puxi, one right on the Bund (Wai Tan), the other near Yu Yuan. The ferry runs until 9:30PM, so it may not be the best choice for a night on the other side of the city, but it is a great way to see the night skyline.  There are two kinds of ferries, the “air conditioned” ferry, which is nicer and has more plush seats, and the standard ferry.  The standard ferry only has seats around the edges of the boat, and many commuters ride this ferry with their bicycles or scooters for a nominal extra fee.  The ferry costs between 2.5 and 5RMB ($0.40 and $0.80).

Buses run the whole range of the city, and it's useful to have a transportation card because they do not give any change. If the bus costs 1RMB and you have a 5, you can wait at the front of the bus and try to swap for coins with oncoming passengers so long as the bus driver has clear site of you. There are particular centers of the city that are teeming with buses where you can be sure to find one that will reach your destination the most useful for seeing the sights of the city are People's Square, Jing An Temple, Wai Tan, Xu Jia Hui, Lu Jia Zui, and Gu Bei.  The key to the bus system is figuring out which stop it is, and which stop to get off.  This isn't impossible for a non-Chinese speaker (or reader) so long as you have a good idea of the bus routes that are useful to you  (don't forget, you can learn this from a good map or a good concierge).  Bus stops are named by road, or sometimes by an interesting site, or by an intersection name, so it is not predictable. Many of the newer buses actually have flat plasma screens showing “Shanghai Mobile TV,” one of the station specialties broadcast from the Oriental Pearl Tower.

The subway is the most manageable of all the transport methods regardless of language because there are fewer stops, and it is easy to learn what parts of the city can be reached.  The subway (Di Tie) and light rail (Qing Gui) have been grouped together as one unit with transfer tickets available, though locals find the light rail less dependable.  The subway fare is rated by distance from point of origin, costing 2 to 5RMB.  Details on the subway have been translated into English: Urban Rail English

Note that some of the stations shown in the map have recently had name changes - On Line 2 (Green) Shi Men Road has been renamed West Nanjing Road and He Nan Zhong Rd has been renamed East Nanjing Road. 

There are "touch" screen ticket machines that you can purchase your ticket - the word "English" is on the top right of the screen - by selecting that all the instructions change to English
- you select the destination line (bottom left) then a map of all the stations on the line and their names are shown                                       - you select the station and the "single" fare is displayed (along with the numbers 1 to 9)
- the numbers 1-9 are to indicate the numbers of passengers traveling (it defaults to 1)
- by selecting 2 it then automatically increased the price - to that for two travelers.
The machines took notes as well as coins - and gave change.

Entry to the trains from the platform is very easy - yellow lines are painted on the platform where the carriage doors open - so you stand to the left and right of those. The seats in the carriages  are parallel to the carriage wall  - so  there is plenty of standing room  (and room for suitcases).
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.