Make sure to get a business card from the recruiter or a contact person. After the fair, do not wait to be called. Be pro-active and contact the companies you are interested in. Remember you only need one good job offer. It may take several tries before you get it.
Most graduate students teach during their first year or two of graduate school.
Some students end up teaching their entire graduate career. While teaching is excellent experience, obviously one's research and hence graduation will progress faster if one is focusing solely on research. These fellowships are highly competitive, but if you get one, they will make your life a lot easier. They have a number of exciting events coming up this Fall. GRE Study Session - The graduate record exam is required for admission to most graduate schools.