Many airlines fly into Shanghai, as it is the international city of China. Some recommendations are:
International fliers will fly into Pudong National Airport, located in, as expected, the Pudong District.
Travel tip: Make sure to book your flight at least 45 days in advance to get the best prices. Or, you can take a risk and book at the last minute, sometimes airlines drop their prices extremely close to the departure date in hopes of filling up empty seats. I would recommend against this method, unless you’re very good friends with a travel agent who can book you seats the instant they receive the notice of a massive price drop (agents get airline prices before the general public do).
Shanghai is big. I would recommend against traveling solely by foot. That would only result in blisters and ruined shoes. Taxis are everywhere in the city, prices start at 12 yuan (around $2), and go up according to how far you travel. As mentioned before, the drivers speak limited English, so make sure to write down where you want to go in Chinese so that the driver can understand where you want to go.
The Shanghai Metro is also relatively easy to navigate: lines are color coded and all the stations are listed in both Chinese and English. The metro lines have expanded because of the Expo, so the city is even more convienent to travel around in. Ticket prices are by distance, so the farther you want to go the more the price of the ride will be. The major downside to the metro is that almost everyone takes it: expect a lot of pushing, cutting in line (there are markers that tell you where to line up, but most locals ignore them), and scrambling for seats. Also, don’t try to hold the doors; they don’t respond to blocking. If you arrive at your stop but are unable to get out, just push through the crowd. If you can say “excuse me” in Chinese (either duibuqi or buhaoyishi), go ahead. Otherwise just push, the locals won’t be offended and consider you rude.
I recommend against taking the bus, as there is no English bus map and the routes are confusing. If you really do want to take a bus, this site has a list of all the bus routes in English. The problem with that directory is that you have to go through every route until you find the one you are looking for, and there are hundreds of bus routes in Shanghai.