The London Underground, or Tube, as the locals call it, is one of the largest and most extensive subway systems in the world. It may seem like you would be lost in these mazes of tracks and tunnels, but it is surprisingly easy to navigate. Each "line" is displayed in two ways; one is by color, the other is by its name. This makes it easy to pick out that the "Picadilly Line" is "Blue". The Tube is also structured into zones, but you will not need to worry about that unless you venture outside the major sites of London. In order to determine which way you want to go, you can either select the endpoint of the line in the direction you want to go or look at the line maps that are at each major "fork" in the path. The map will show the name and color of the line along with an arrow pointing to which way to go to get to the correct platform. The hardest part is matching your destination to the closest Tube stop, but most maps and guidebooks will give you that information in the description of the site. To make it easy on yourself, go during non-rush-hour times. This way, you will not hold up traffic or feel rushed.
A couple of major things to remember:
Each trip, including tranfers in the same trip, costs about $3.75. The 7-Day Unlimited Travel Card costs about $23 for Zone 1 (Central London), which is where most of the things you want to see are located.
The Tube runs all the way out to Heathrow Airport and takes about an hour to get into the center of London. It is a nice ride since most of it is on the surface. Talk to the people at the Customer Service Desk and they will help you find what you need.
If you intend of riding the Tube alot, buy a Travel Card for the number of days you will need it. It is good for unlimited use and will save you quite a bit of money. You can get these tickets at any major stop as well as the Heathrow Airport terminal.
Always keep an eye on your bags and be aware of your wallet. While pickpockets are not as out of control as they are in Italy, they are still around. Just pay attention and you will not need to worry.
The Tube is great for traveling longer distances, but will be a pain for short ones. If you need to go one or two stops over, walk! You will see more of the city this way. Otherwise, take the Tube and enjoy the ride.