The expiration date on the visa does not have any relationship to the length of time you can stay in the U.S., only to the length of time it is valid to present to immigration when applying for entry to the U.S. The duration of your legal stay in the U.S. will be noted on your Departure Record, also known as Form I-94.
Form I-94 records your arrival date in the U.S., the type of visa you hold, and your expected date of departure from the U.S., and should remain in your passport until you depart the U.S. F-1 and J-1 visa holders will get a notation, D/S, meaning duration of status.
When you completed the I-94 upon arrival in the U.S., you also gave your initial address in the U.S. If you are subject to Special Registration, you must remember to complete form AR-11 SR every time you change your address after your initial entry to the U.S. For all other F-1 and J-1 students, you must inform the International House of any address change in order for us to update your SEVIS record.
H and O visa holders must complete form AR-11. With the latest changes in immigration regulations, it has become very important that you maintain your status; failing to do so can have serious consequences, including being denied entry to the U.S.