Japan, especially Tokyo, has a dense public transport network. There are countless number of lines such as the Yamanote, Chuo, Sobu, and subway lines like Hanzoumon, Chiyoda, Hibiya, etc... 

I've been living in Tokyo for 10 years, but I definitely can't memorize all this. So that's when I use train route finder websites like below. I usually use just one of them, but incase some of them are accidentally out of service, I'll give you a few choices.

Do take care, if you are looking for a long-distance route, these websites may use limited express trains. This will be indicated by "Express Surcharge". If you see a fee in this line, that means you need to purchase extra tickets for these trains before you get on. Make sure you have enough transfer time for this!

Jorudan

http://www.jorudan.co.jp/english/

All you need to do, is enter the train station you are departing from, and going to. It gives you various train route options, such as cheapest / fastest / easiest (least transfers), etc. I use this most of the time. 

HyperDia

http://www.hyperdia.com/en/

I didn't know about this service before writing this article, but it seems to be a website run by Hitachi, one of the largest heavy industry manufacturing firms in Japan.