JR has a discount for students taking the shinkansen or other long travel train (the train needs to exceeds 100km). You need a special paper to access this discount. To use them you need to fill out information about the trip like departing and arriving station as well as if it is one way or round trip. With this you will get 20 percent off the fare, but you can only get 10 trips papers per year.
At Ritsumeikan Univerity: You can get them from the back of Shitokukan. They have a machine that issues certificates. First use your ID card to sign in then pick Certificate in Japanese or English and there will be the button for Discount JR (JR gakuwari). Then pick how many you wanted printed and what the reason is then the machine will print them out.
An example photo can be found here.
Kyoto Student Guide 