There are many ways to get around Tokyo. Hopefully, you will be staying at a place near a station on the Yamanote Line. This is a circular line that runs around the heart of Tokyo. It stops off at many of the tourist sites and hot spots in town. If its not along the Yamanote, then its a short ride from one of the many stations situated on its route. As a newcomer, you cant get lost on this green-colored line. If you happen to take the train in the wrong direction, sit back and enjoy the view as you will eventually get to where you want to go
Here is a link to a pdf file that shows all the JR lines in Tokyo. Mind you, this just shows the train lines and not the subway