I will assume that you already know your destination and local nearest station. If you have internet availability, pull up Hyperdia.com to find the best route, and print that out or write it down, the important things to note are 1. The line name 2. The direction of the trains 3. Transfer stations. If you don’t have internet, or access to internet, there are information desks in all train stations, as long as you have the station you want to get to, they can help you out.
Next make your way to the nearest train station, look for a large map on the wall, under it will be ticket machines, there is a handy English button on all of them, so for the most part they are really easy to use. There will be a large range of ticket prices, I recommend paying the smallest amount, and then paying the difference at your destination, otherwise you run the risk of over paying.
Once you have your ticket head to the gate, there will be a slot for you to grab your ticket at the other end, make sure you grab your ticket, otherwise you can get in a lot of trouble, and sometimes will have to pay a large fine.
Next find the direction you are going, today we are headed to Hachioji, which is listed on the sign (if we were headed to Sagamiko, which is in the same direction, we would have needed to have known to catch the train in the direction of Hachioji and Shinjuku, which is in the same direction).
When the train arrives be sure to stand to the side of the door so that passengers can exit first. If you are in a really rural area there may be buttons to the side of the door that you have to push to open the door.
On the train listen for your stop, usually the train will inform you in both English and Japanese what the next station is. If you couldn’t understand, look out the window for a sign that has in big letters, the station you are at, and the name of the next station and previous station written in appropriate directions.
If you have to transfer, you do not need to get a new ticket, just go to your new track, and continue on your journey. If your transfer requires that you change train companies (example: a JR line, to a Keio Line) then you will have to pay, and get a new ticket.
Once you have arrived at your station, take your ticket to the Fare Adjustment machines (usually near the exit gates, and well labeled). Select English language, and then insert your ticket. Pay the extra amount, and then take your ticket to the exit gate. Insert your ticket into the machine, and then leave, you will not get your ticket back.
It sounds more complicated than it is, good luck!