It is very easy to get to London Dungeon. I believe the easiest way is to take the underground to London Bridge Station, which you can find on the Northern and Jubilee Line. (See underground)
London Dungeon is almost a trip down history. You are in a small group of people where you are following one of the scary guides and they tell you terrifying stories from a long time ago. They are involving the people, sometimes a little too much in my opinion. I have to admit that I was quite scared when they put me in a cage and I was sure that something was going to happen to me. (This was the part when Kjell Steinar could not protect me.) Thank god nothing did, but I am not afraid to say that I was terrified.
As you are on this tour you get to hear about the Great Fire of London, Jack the Ripper and an anatomy theatre to mention a few. It is quite educational of how London used to be, with a great hint of scariness. The guides are wearing costumes and they are really into their job with telling these stories and scaring us. The tour ends with a drop ride to doom and your last scream of the day. I was very impressed and I can understand why this is a popular tourist attraction here in London.
Even though I get very easily frightened I absolutely do not regret going to this. It was a lot of fun and I would totally recommend going here. I would say that it is not suited for young children and people who get nightmares. Other than that, enjoy the tour!