Taxis: Be prepared to get ripped off! We took a taxi to and from the airport and we were over charged almost double. Also, if you value your life, please put on a seatbelt.
After our near death experiences in both taxis, we would not recommend them but sometimes they are your only option (ie. when you have 6am flight!)
Our best tip would be to have a map/ google maps/ GPS or at some sort of idea of where you need to go so they don’t drive around in circles and rack up the meter.
Buses: Within Shanghai itself, buses are easy to navigate and cheap at 1-2RMB/ AU$0.20-0.40 per ride