Get an oyster card! You will most likely use it everyday. Oyster cards work for both the tube and bus system. I bought a student oyster card, which is cheaper so make sure to apply for one. You can either pay per month for an unlimited number of uses, or pay as you go (add money and it will deduct during every use). I had the unlimited because I was using the tube/bus at least 10 times a week.
Use a cab if necessary, but cabs can get pricey.
Uber is great and not as expensive as a cab. Make sure to download the free app on your phone.
There are 5 London Airports: Heathrow, Gatwick, Luton, Stansted, and City Airport. You can take the tube (Piccadilly line) to Heathrow and (DLR) to City Airport. The other airports you can take a train. Most of the airports via tube/train are approx. 30-50 minutes away. You can also take a bus to various airports for a cheaper price but it will take longer.
You will want to walk a lot in London because there's so much to see and you will become more familiar with the city. Make sure to bring comfortable walking shoes.