Actually, and despite the fact that services are provided by more than half a dozen independent companies, it's quite easy to navigate. Even when you run into vertigo when seeing it for the first time.
Each line, no matter if Tokyo metro, private metro, JR, private railway is color coded and has a fixed one or more unique letter designation.
Say, you want to go to Ginza, to just take one example. You don't even have to remember the station name. You just need to know the station codes. In this case M16 (red), H08 (gray) or G9 (orange). The letter designates the metro line, while the number represents the station for the respective line. And each combination is unique.
That, in combination with a PASMO or SUICA smart card makes orientation very straight forward and seamless.