I currently live in East London, so I take public transportation into Central London in order to attend class almost every day. In London, there are three main forms of public transportation. The first and most popular is the underground, (better known as the "Tube". The Tube is like the subway in New York City, but it is actually tube shaped! The Tube is the fastest way to get around the city. Next is the overground, which is pretty self-explantory: it is a train that rides above ground. Some routes require taking the tube for the first part and taking the overground the rest of the way. Lastly is my favorite (and the cheapest) form of transportation, the double decker bus. There is nothing like riding on the top level and watching the city from above.
Most people take one of these three forms of public transport, but there so many additional ways to get around. You can uber, taxi, drive or ride your bike just about anywhere in London.