Wow, good question O.o However, I don't think this is a Debate question! I'm going to move this somewhere more appropriate.

The Influenza Vaccine is made like any other vaccine: it contains the virus it intends to protect you from. The virus is dead or very weak so that your body can identify it, fight against it with minimal side effects, and be ready in case you ever contract the actual flu. You can't catch a disease you've already had, so by injecting a vaccine and having your body identify it, you are protected against contracting the flu.

This is the actual process for making the Flu Vaccine:
Flu Viruses type A and B are grown starting in late summer in the whites (albumen) of chicken eggs. This process takes about two months. The viruses are then extracted, purified, killed, and dispensed into vials.
Thimerosal (a mercury-based preservative) is used to preserve the vaccine on shelves so it can get to the people who need it.

There are two types of flu vaccines, the flu shot which has an inactivated flu virus and the nasal flu mist which has the weakened virus.

You cannot get the flu from the flu shot-- the virus is already dead. Your body will make antibodies against the many epitopes (distinct features) of the influenza virus and thus you are protected if you encounter a live virus later on.

The nasal flu mist is a weakened virus but it is very unlikely you will get the flu from the flu mist unless you are immunocompromised (HIV, cancer, recent transplant). It is not reccommended for pregnant women or children. They should take the flu shot instead.