Getting to and from Shanghai is easy with international flights east of the city at the Pudong Airport, and domestic flights on the west of the city at the Hongqiao Airport. Nowdays many domestic flights are moved to Pudong Airport. If you are going to do domestic flight, be careful which the airport you will take off. Hongqiao Airport is about 5-10Km far away from the downtown center, while Pudong airport is about 50-60Km far away from the downtown center.

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 19-25RMB ($2.00-$3.00).  Pudong Airport provides several routes of Airport Express Bus to connect the Airport and city downtown. It costs only 20RMB (less than 2.5$). One of the route connects the Pudong Airport and Hongqiao Airport. The economy way is to first take the Airport Express Bus to city downtown and then take the Taxi. Several hotels have a small stand between the customs area and the exit, be sure to check with them for easy transportation. If you take a taxi from the airport to the downtown area, be sure to ask what the fare will 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. 

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 on north into Russia.  Shanghai's train station lies on the north side of the city, and is a main focus 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.

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 is not the clearest. The easiest directions are - 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 direct you along the "long" walk way 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.

Exiting from the Longyang Road (Maglev) station and transferring to the Longyang Road Line 2  station is very easy -  the escalators 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. .