The great thing about the subway in London (also called the Tube or Underground)  that makes touring the sights easy for  visitors is that  the London Tube will get you anywhere you need to go in  the city.  
  
In the Zone
The London Tube transit system is  laid out like an onion.  Zone 1 is the  city center and includes nearly all of the main tourist sights, such as Big Ben  and Buckingham Palace.  Zone 2 is the  next layer. Zone 3 and higher are the suburbs.   Most tourists tend to stay within zones 1 and 2.
  
Choose a London Tube Pass Based on Your Length of Stay
It's possible to buy individual tickets for each London Tube ride but that can quickly become expensive.
Tidbits
       - The London Tube is the world’s oldest and longest underground system. - It opened on January 10, 1863. - 3 million people ride the Tube everyday.  | 
  
That's why, if you are in London for   three days or less, your best deal will be the Travelcard.  You can get a London Travel Card in increments of one or multiple days. With it, you can take unlimited rides on the London Tube in any direction   within specified zones. 
If you are in London for  a week or  more, then  the Oyster Card is for you. The Oyster card is reusable and you pay for only the amount you need. The Oyster card never expires.
Keep your Oyster card for as long as you're in London. Whenever you use up your amount, you simply replenish the balance on the Oyster card.
Both the Travelcard and Oyster card can also be used to ride the buses.
Another Option
Another option is the London Pass, which includes unlimited rides on the London Tube as well as skip-the-line entrance to certain tourist sights and museums throughout London.
To ride the London Tube, first grab a pocket Tube map from the information booth. Determine to which station you need to go. The lines in the system are denoted by a color and a name.
Once you enter the station, touch your Oyster card or Travelcard to the top of the circular card reader on the turnstile. Hang on to your card because you will need it to exit the station.
Follow the signs to the platform that corresponds with the tube line and direction you need to go. Signs throughout each station show the stops for the lines passing through that particular station.
One more thing, if you are taking a Tube line that splits into two directions, check the name of the last station on the line you want.