Everybody should network and we all do to some extent starting when we are little kids at birthday parties, sleep overs, going to pre-K and during all the others phases of our life.
There are 4 important benefits from networking: accelerating your own career (whatever it is), having a positive impact on the organization with which you are working, enriching your personal life and enhancing the lives of your family and friends.

Most people get a little edgy in the situation you describe. A few tips include:
•    Do your homework ahead of time. Try to get a copy of the attendee list and, if it relates, names of the sponsors and speakers. Then decide who you might want to meet. Google or look them up on Linkedin and then reach out to try to schedule time to meet at the event.

•    Show up early , rather than on time or even a little late. If you are early showing up at the event, before it gets crowded, you can spend time with the few people also showing up early. Those coming after you will have to break into your conversation vs. the other way around.

•    Practice your 30 second profile ahead of time so you are well prepared to quickly and accurately introduce yourself at the event.

•    Start networking at the event by singling out someone standing by herself or himself and introduce yourself and start a conversation. It’s easier to warm up by focusing on a single person than by trying to break into a group discussion.

To us it makes sense to be ready to network with everyone you meet and in each situation be prepared to discuss both personal and professional topics. This means, among other things, to always have your business cards with you.

People are people. Generally we all are interested in many of the same things. People you meet, regardless of who they are, are likely to appreciate hearing of simple things like a good restaurant, a bottle of wine, a movie or play you have seen, a book you have read or a B&B. From a strictly business point of view maybe you can suggest a good strategic contact for the new person you met.

Today, having an on-line presence is part of your personal brand. From a professional perspective Linkedin is the social media platform to use. It is where people will turn to learn about and check you out.
Make certain that your Linkedin profile is robust and kept current. A few minutes a day or a week is all it really takes for you to have significant Linkedin presence. Of course, use Linkedin to connect with people you meet. Remember, connecting on line is more about connecting with the right people than it is about connecting with as many people as possible.

Going through life we all develop “clusters” of new contacts, some of which we value more than others and with whom we want to build strong relationships. The “clusters” in which you can network include your college contacts ( all of them including students, faculty, administrators), people with whom you work or meet through your work, neighbors and others in your community, members of various clubs or charities in which you are involved.
Spend a few minutes defining your “clusters” of potential new contacts and then start thinking through how you can initiate a connection with the people you would value in your “clusters.”
Other than networking within your “clusters” don’t hesitate to randomly start talking to the people you meet just in the course of your every-day life, i.e. in the check-out line, at your doctor or dentist office, sitting next to you on a bus, train or plane, shopping in a book store or while waiting to have your car serviced. Randomly meeting new people may not yield a high percentage of new contacts that you want to develop long term but it is certainly great practice for building your self-confidence re: successful networking.