If you're Wimbledon-bound and don't live within walking distance, the London Underground -- commonly known as the Tube -- is the most painless way of getting to the All England Club.
Fans take the District Line train toward Wimbledon. If you need to transfer, the easiest place to do so is at the Earl's Court station. Expect the platform and the trains heading this direction to be packed. At times, you might have to wait for another train to come in, as there's not an inch more space for someone to stand. If you want to know what it feels like to be packed in like a sardine, this is your perfect experience.
Here's an interesting little factoid for those coming to Wimbledon for the first time: You actually don't take the train to Wimbledon. You get off at Southfields, which is the community before Wimbledon. Don't worry about getting lost -- it's impossible.
The train announcer will tell you repeatedly, “If you're going to the championships, alight at Southfields.” Alight isn't a word often used in American English vernacular, but the British love it.
When you get off, just follow the crowd. The walk from Southfields is shorter and easier than from the Wimbledon station, which would require you to be a mountain goat, as hill walking is required.
And by the way, when you get off the train don't forget to "mind the gap" -- you'll be told to do so, as they don't want anyone falling onto the tracks.