Tokyo has one of the most complex and busiest train- and subway system in the world. They are owned by several different companies, mainly: Japan Railways, Toei, Tokyo Metro, Keisei, Tokyu, Yurikamome, ...

This map may look as daunting as looking at the London Tube map, but there are some helpful hints to make it easier.

Train lines

The heart of the whole system is the circular JR Yamanote Line (its route is even shaped like a heart ;p). This line connects all the major neighborhoods in Tokyo: Shinjuku, Shibuya, Akihabara, Tokyo, Shinagawa, Ikebukuro, Ueno (to name a few). It has 29 stations on its route and one roundtrip takes just above an hour. There are trains arriving every 2-3 minutes in both directions, and has about 3.5 million passengers every day on 29 stations. (as a comparison: the New York subway has 5 million passengers every day on 26 lines and 468 stations) This makes the Yamanote Line the busiest trainline in the world. But it is also one of the most convenient when traveling around Tokyo. Every other trainlines or subway that goes through Tokyo crosses one of the stations on the Yamanote line. Many trains connecting the Yamanote line go deep into the Japanese main land.

The second most important lines are the Chuo Main line and the Sobu Main line, these 2 lines run horizontally through the center of the Yamanote line circle.

Another important trainline is the Keihin-Tohoku line, this one goes from Yokohama to Saitama and does the major stations of the East side of the Yamanote line circle.

Subways mostly run inside the Yamanote circle with some going further outside the circle usually above ground. The oldest subway line is the Ginza line which goes from Shibuya through Ginza & Ueno to Asakusa.

Stations
Shinjuku station is the busiest station in Tokyo with 11 lines going through it, 35 platforms of different levels and having an average of 3.3 million people every day. It is also the second largest station in the world after Nagoya station in terms of area. It has well over 200 exits and large shopping malls above it. Shinjuku stations handles traffic between Tokyo and the western districts.

Ikebukuro station is the second largest commuter station in Tokyo (& the world) with an average of 2.7 million people on weekdays. It serves 8 trainlines. It handles commuter traffic between center city and Saitama and suburbs in the northwest.

Shibuya station is the third largest commuter station in Tokyo with 2.4 million people on an average weekday. It generally handles commuter traffic between center city and suburbs to south and west.

Tokyo station is a large station that is the starting point of the Shinkansen trains bound for southern Japan.

Ueno station is the traditional arriving point when coming from Narita airport and the starting point of the Shinkansen trains bound for northern Japan.

Downloads

I have some pdf's here that I found around the internet for you to download.
Tokyo Trainmap (don't remember where I got this from, so can't credit)
(made by Bright International)