Getting to and from Shanghai is easy with international flights east of the city at the Pudong International (PVG), and domestic flights on the west of the city at the Hongqiao International (SHA). Currently, some domestic flights have moved to Pudong Airport. If you are going to be flying on a domestic flight or some flights to Korea and Japan, please confirm the airportfrom which you will be taking off. Hongqiao Airport and Pudong Airport is about 5-10 km and 50-60 km from the downtown center respectively. See:  Official Airport Infomation

Both airports have taxi queues and a shuttle bus system to help you get into the city.  Many of the bigger hotels also have a shuttle bus system that is either free or costs 19-25 RMB ($2.00-$3.00). Pudong Airport provides several routes of Airport Express Bus to connect the Airport and city downtown. It costs only 20 RMB (less than $2.5). One of the route connects the Pudong Airport and Hongqiao Airport. The economy way to the downtown area is to take the Airport Express Bus to the city downtown and then change to a taxi. If you take a taxi from the airport to the downtown area, be sure to ask what will the fare be. The driver should charge you by the meter which usually is about 150 to 200 RMB, do not accept a flat rate as the airport is a significant distance from downtown and it is difficult to judge a reasonable price. 

NOTE: 'Several hotels have a small stand between the customs area and the exit, be sure to check with them for easy transportation.'  Hotel shuttle bus services have been cancelled from 1st Jan 2008, refer to the airport information website for details of this notice.

There are three long distance coach bus stations (two near the train station) offering transport to different parts of the country.  Trains connect Shanghai to the rest of China, Hong Kong, and north into Russia.  Shanghai's train station lies on the north side of the city, and is a main focal point for the public transportation system. 

Be patient in determining where you are going to and coming from, and always be sure to leave extra time for traffic. Shanghai has an expressway system through and around the city, but rush hour is the same in China as it is anywhere else in the world.

If you want the experience of traveling by train at 400 plus km per hour then take the Maglev train from Pudong Airport to Longyang Road.

The website for the train is - http://www.smtdc.com/en/index.asp

Once you come out into the airport arrivals hall - the signs to the train are not the clearest. The easiest directions - to the left of exit door 8 (from the airport to the street) are three passenger lifts - take one of these to the second floor. When you exit the lift, the signs will direct you along the "long" walkway to the Maglev station.

In the Maglev station the normal fare is 50 RMB, however if you produce your "arrival plane ticket" the journey will cost you 40 RMB. (The same discount is available for the journey to the airport).
Refer - http://www.smtdc.com/en/jszl.asp

Traveling at 430 km per hour by train is amazing. There is an electronic clock and speed indicator in each compartment.

It is easy to exit from the Longyang Road (Maglev) station and transfer to the Longyang Road Line 2  station -  the escalators will take you from the platform to the ground floor and you walk under cover across to the line 2 station.

Traveling on the underground is really easy, with the ticket machines being touch screen and having a button for "English" in the top right corner of the screen. .