If you are planning to stay in Shanghai for a relatively long period of time, it would be wise to buy a rechargeable Shanghai Public Transportation Card which can be used to pay for subway, bus, ferry, and taxi rides. The card can be purchased at any subway station.
Shanghai by subway
The subway is Shanghai's fastest and most efficient form of public transportation. It stops at all main attractions and commercial areas and it’s pretty easy to navigate. The stations are clean and there are maps in English and Chinese. But it has its disadvantages as well - at peak times (7am-10am and 5pm-7.30pm) it can get extremely crowded. Also, the subway stations close before midnight every night.
For ticket prices and exact closing times, take a look at the following website
: http://www.shmetro.com/node155/node158/201004/con103690.htm
You can find a good subway map here: http://www.exploreshanghai.com/metro/
Shanghai by taxi
Taking a taxi is a fast and convenient way to get around Shanghai. There are approximately 45,000 taxis, operated by over 150 taxi companies, which explains all the different colors of the taxis. An official taxi has a meter, taxi driver registration or license and a vacancy disk. If your taxi doesn't have all of these, it’s probably unlicensed! Do not take unlicensed taxis, because the drivers overcharge, and you have no rights if injured.
In some taxis you will find a certain amount of stars just below their registration number. The number of stars denotes the quality of their service. More stars indicate that the driver knows his or her way around Shanghai very well, understands some English, and drives safely.
Taking taxis in Shanghai is more expensive than in other Chinese cities. During the day (5am-11pm), the price is 13 CNY plus a fuel surcharge of 1 CNY for the first three kilometers. An additional price of 2.4 CNY is charged for every succeeding kilometer within ten kilometers and 3.6 CNY for every succeeding kilometer after ten kilometers. At night (11pm-5am), there is a 30 % night surcharge. So the price is 17 CNY plus a fuel surcharge of 1 CNY for the first three kilometers. An additional price of 3.1 CNY is charged for every succeeding kilometer within ten kilometers and 4.1 CNY for every succeeding kilometer after ten kilometers. Five minutes of waiting time costs the same as one kilometer.
Taxi drivers usually ask “Shénme lù” (什么路), which literally means "which street". The streets in Shanghai are very long, so it’s better to mention two streets, namely the main road and the closest crossing street. If you don’t speak Chinese, print out the address in Chinese characters to hand it to the taxi driver. Unfortunately, some taxi drivers can’t read, so it’s always useful to take a map with you. Then you can just point to where you would like to go.
Remember to ask for a receipt (发票; fā piào)! They contain information on the taxi, such as its plate number and the taxi company. If you leave something in the car, or have any complaints, you can call the company. Although you have no guarantee of getting your things back, it certainly doesn't hurt to try.
Shanghai by bus
Buses in Shanghai are identified either by numbers or Chinese characters. So if you already know how to read Chinese, you're in luck. Otherwise, check out this website, which has the routes in English.
There are 9 different numerical categories:
• Line numbers under 200 are conventional buses. In these buses, lines under 30 (except those starting with 0) are trolleybuses. All trolleybuses are now air-conditioned
• Line numbers between 200 and 299 are mostly rush hour lines
• Line numbers between 300 and 399 are night buses
• Line numbers between 400 and 499 are cross-river bus lines
• Line numbers between 500 and 599 are special-line connecting buses
• Line numbers between 600 and 699 are special-line buses in Pudong.
• Line numbers between 700 and 799 are suburban conventional lines.
• Line numbers between 800 and 899 are special-line buses serving between downtown Shanghai and the outskirts. Most of them are mid-size buses, but now they are being replaced with air-conditioned large buses
• Line numbers between 900 and 999 are special-line buses. Most of them are full-size and air-conditioned.
Ticket prices vary depending on the category of the bus line and other conditions, but one ride typically costs 2 CNY. Tickets are purchased on the bus. You can pay with your Transportation Card or insert coins into a steel collection box next to the driver. Sometimes, there is a conductor on the bus. Most buses running on downtown streets are self-service with no conductors. So make sure to have some loose change, because the bus drivers aren’t allowed to handle cash.
Shanghai by foot
In China, cars are not required to yield to pedestrians. So the moment you 
step outside and onto the streets, you really need to watch out. When crossing a street, a green pedestrian light doesn’t necessarily mean it’s safe to cross the street. Check all directions of traffic, because cars will not stop for pedestrians even when the pedestrian is obeying all laws. Furthermore, there is a traffic rule that allows cars to turn right, even when the traffic light is red. Never let your guard down when navigating the streets of Shanghai.
Shanghai by bicycle
In Shanghai, riding a bike is a common, inexpensive way of getting around. But be careful! Riding a bike can also be very dangerous. The roads are crowded and can be extremely chaotic. Cars, motorcycles, and mopeds do not follow the traffic rules well, making cyclists vulnerable to accidents. There is still a long way to go for Shanghai's bicycle environment.
You can rent bikes very easily (for example, through China Cycle Tours and Giant bike) , but if you stay for a longer period it’s better to buy one. A new bike costs around 180 CNY and up. For about 50 CNY and up, you can get a used one. Always make sure to lock your bike, because bike theft is very common in Shanghai.