The "new" (As of 2000) Shanghai international airport is located in Pudong east of Shanghai, on the opposite side of the city from the old airport in Hongqiao (many domestic flights, including flights to and from Hong Kong, still go to Hongqiao).
As it is a new airport, it is very clean. The ceilings are very high so there are a lot of echoes. This airport is a lot better than the old airport, which was often overcrowded; however, the downside to having this new sparkling airport is that it is located right smack in the middle of nowhere, at least a half hour away from the city.
There are at present 3 ways to get from the airport to the city. the first way to get to the city is by cab. In the old days when the planes went to Hongqiao, this was definitely the way to go, as it was convenient and not too expensive; however, a cab from the new airport is rather expensive (for China standards, probably between $15-20 and up, whereas a normal cab ride in Shanghai is maybe $2-5 and other). The second option is to take a bus. There are five routes from the airport and prices are a lot more reasonable, also the buses are new and comfortable (and air-conditioned) The final option is to have a car, which not too many people have access to.
There are plans to extend line #2 of the Shanghai subway so that it reaches the airport. I have also heard that the Shanghai government has made a deal with a German firm to build a high-speed maglev train between the center of Shanghai and the airport. The train would open in 2003.
If your bags are too heavy, you can pay off the airport attendants to run your bags through anyway- 50 to 100 yuan should do the trick. 50 to 100 yuan is only US $6-12, which is a lot cheaper than paying big money to send your overweight bag to wherever you are going.