If you are traveling on some rural train lines, you need to push a button to open or close the door. Even Japanese riding for the first time stand in shock why the door is not opening. Also, make sure to push the close button after you enter to keep the temperature inside comfortable.
Other than that, avoid running on the train platform as it is dangerous!
Let me just add to some of the already mentioned tips:
- Do not stare at other passengers.
- If you have a big bag, make sure it does not block the way or it doesn't touch (or inconvenience) the person sitting next to you.
- Snacks are okay provided that it doesn't create too much noise when you chew them, or that they do not have a very strong smell that may inconvenience others sitting near you.
- If you are with a friend, avoid loud conversations and laughters.
There is many, there was posters by Tokyo Metro, they are really nice, basically, it's the same simple rule in examples "don't invonvenience other people".
Note : the first poster is a parody : http://gakuran.com/36-iconic-tokyo-metro-subway-manner-posters-2008-2010/