SSN is the number assigned by the US government to citizens and
some residents for the purpose of tax and social benefits. It has
been widely used by the country as the identifier of people.
As a F-1 student, you are entitled to a social security number.
Your school may have invited the social security administration
to come to the campus during the international students orientation.
That would be the easiest way for you to apply for a SSN. Otherwise,
ask for the location of the nearest Social Security Administrations
office and go there to apply.
To apply for a SSN, you need to bring your passport, and have your
address and home phone number ready. A social security card will
be mailed to the address you provided. The card doesn't have your
picture, and usually cannot be used as ID card. But it will be needed
each time you start a job, to show your eligibility to work in the
US, and for the employer to report salary and tax information to
the Internal Revenue Services.