Getting Around

Subway
Shanghai only had 2 lines back in 1999 but now has 18 lines as well as a link from Hongqiao Airport to Pudong Airport. In other words, it is a very efficient way of getting around the city. It's also very affordable, at least compared to say, London. Short trips cost just 3 RMB while longer trips cost up to 8 RMB.
The Explore Shanghai app is a great way to navigate the subway. It has routes, trip times and fares in English. Highly recommended.
You can buy tickets from the machines using cash or you can buy a travel card which you can top up with credit when needed, which would be the best option if you are going to be using the subway often. The card also works on buses and if you use an iPhone, you can use Apple Wallet and avoid having to carry a physical card.
The main drawback of the subway is that it can get very crowded at peak times, but other than that, it is a great way to travel around the city.
Didi
Hailing a taxi on the street is difficult these days because everyone uses ride hailing apps for taxis and other cars. Didi (a Chinese version of Uber) is by far the most widely used throughout China, so if you only download one ride hailing app, make sure it is Didi. The good news is that Didi has an English interface which you can choose within the app in the settings.
You can use Didi to hail taxis as well as cars covering all levels from economic smaller cars to 7 seater Buick GL8 type vehicles if you have a larger group or just like to travel around in a bigger car. Fares are very reasonable - expect to pay less than 20 RMB for a typical short trip. An airport run will cost you from around 160 RMB, depending on the class of vehicle.
Shared Bikes

There are several companies offering shared bikes all over the city and they are very easy to find and use. Unlike some countries, you can just leave the bikes anywhere and do not need to return them to specific stations. You will need to download the Meituan app or use Alipay to scan the QR codes on the bikes in order to use them. Costs are very affordable and depend on the amount of time your journey takes. Shared bikes are great for those journeys that perhaps are too short to take a Didi, but too far to walk.