A short description on how to use the subway system in Tokyo.
First locate a map that displays the subway system, you can find one in each subway station, and some of them have English text on them. You can also get a copy of the subway map at many hotels. Find out what line you want to go with, and check if you need to switch to another line at a specific station.
Then locate the board that says how much you need to pay to get to a certain station. The board has a list of all stations, and how much you need to pay. It's usually something in the range 160 - 200 JPY.
Buy the ticket in one of the ticket machines next to the map/information board. The machines have a button that says English. Press that button. Then touch the button with the amount you want to pay and insert money into the machine. You will get money back if you don't have the exact amount. Do also note, that you can adjust the price when leaving a station if you haven't payed enough. I.e you don't need to worry if you by accident doesn't pay enough because you can't figure out the price. The ticket that you get looks something like this.
Insert your ticket into the gate to the subway. Note that the ticket will pass through the gate, and that you should collect it at the other end of the gate. You need the ticket to get out of the subway. Getting out of the subway is done by doing the same procedure as entering, except that the gate will then keep the ticket.
Walk down to the platform. You need to know on what side of the platform you should get on the train. You can get that information by looking at information displays, billboards or signs that says something like 'this side takes you to X, or you will reach stations M1-M15 from this side'. Each subway station has at least one number. Subway stations that serve several lines, has one number for each line.
Another information board, that also shows where you can switch to other lines.
Get into the train, and wait for your station. The trains in the subway has eletronical information displays that shows information both in Japanese and English.
Leave the train at your destination, and insert the subway ticket into the gate to get out of the subway. Note that you shouldn't get outside of the gates when you switch to another subway line. You walk between the subway lines on the inside of the gates. Going outside means that you lose your subway ticket, and that you need to buy a new one.