Recruitment or "Rush" as it is known on campus, lasts for about two weeks for all fraternities. Most fraternities will hold rush events during this time which will range anywhere from an info session, a tour of the chapter house, or a full blown wing eating contest. At all of the events, you want to become friends with as many brothers as you can so that you can make the biggest impact on the fraternity. In most cases, fraternities will have about 4-6 rush events with the ones being in the second week invite-only. So if the brothers think that you would be a good suit for the fraternity they'll invite back a smaller portion of the students rushing in order to narrow down their selection. If the brotherhood wants to give you a chance to join the fraternity, they'll extend a "bid", or an invitation to join. You can receive as many bids from the fraternities you rush if they choose to extend them, but of course you can only choose one, or non at all.
During rush, it is highly encouraged for students or "rushes" to visit as many chapter houses as they can in order to get a feel for all the different fraternities out there. Even brothers at rush events will recommend going to various fraternities to get as much exposure as possible. There's also no need to be nervous at a rush event: all of the brothers are just as nervous as you! They want new members just as much as you want to join so there's nothing to be afraid of. Plus with all of the variety that Rutgers has to offer, it is only a matter of time until you find a group of people that you'll feel comfortable calling brothers.