Your tips When transferring to a bullet train in Hongqiao airport station or when transferring to a national flight, strongly consider staying one night in Shanghai so you are refreshed before continueing your journey.
Be sure to pick a nice hotel in the city since many airport hotels seem to have a high rating but do not really live up to their rating.
From Pudong airport, use the Maglev train to go to Longyang road subway station and then take subway line two directly to Hongqiao airport / train station.
My stay in Shanghai was brief but any new traveller will see how immensely huge it is. The subway is an efficient way to get around while remaining cheap. It is mostly in english, making your life easier if your grasp of Chinese is limited. Taxis are also a good option but can be expensive and more difficult to flag down.
Pudong international airport, where most flights will land, is a modern, clean and efficient place with just one downside. It's distance to the city.
However, there are many ways to get from the Pudong airport to the city. Taxi, bus and subway for example. The most exciting and fastest option is probably the Maglev train.
The Maglev train is more expensive than the subway but has the added benefit of taking only 8 minutes to reach the Longyang road subway station in the city. From there it takes about 45 minutes by subway to reach the Hongqiao airport.
The Hongqiao airport services national flights as well as having a huge train station. If you need to travel deeper into China, then you will probably have to transfer to national flights or high speed bullet trains at Hongqiao.