When you arrive at Pudong or Hongqiao airport, apply directly at Ehi Car Rental Service, Shanghai’s first licensed agency for handling and issuing temporary driving permits for overseas visitors. (Their Pudong airport location is here, and Hongqiao airport here.)
The permit is valid for one year and before its expiry, and you don’t need to reapply next time you make a trip to China. According to Ehi Car Rental Service, soon enough online application services will be provided, meaning you’ll have the permit ready to be collected at the entry points before you land. Like all major bureaucratic changes, perhaps give this some time before you invest your time in applying. When we called today, at the same time Ehi was having a press conference to announce the change publicly, the staff at the actual rental counters in the airports were not familiar with the change yet. More updates as we try this.