If the idea of approaching people you don't know intimidates you, begin your networking efforts by seeking out familiar faces, such as relatives and friends. A logical next step after talking with friends and family is to pursue individuals who graduated from your college. Your alumni network can be a gold mine of connections. It exists for the purpose of networking, so contacting an alum out of the blue shouldn't feel like a cold call. After all, they joined the network to make and take such calls.
Introverts and inexperienced networkers often apologize when asking for an individual's help because they see networking as an imposition, not as an exercise in relationship building. Apologizing demonstrates a lower level of professionalism and confidence. You don't have to apologize for asking for help. You don't have to apologize for wanting to learn more about the individual with whom you're networking. One day you may be able to help him / her out.
Use your Instincts
Humans are hard-wired as communal, tribal animals, so the shy person isn't shy by nature. They are shy by design. Something happened to them to make them want to crawl into a shell. Sometimes, when an introvert hears that he's not inherently a loner, that humans are innately social creatures, the realization helps them to emerge from their shell of shyness.
Many introverted professionals think they have to act like an extrovert in networking situations. While you do have to make an effort to be more open than normal, you shouldn't be artificial.
Tap into Your Passions
Join clubs and attend events that relate to an interest or activity you enjoy. If you're a budding oenophile, attend a wine tasting. Eager reader? Join a book club. Can't get enough of all things sporty? Attend a football game or watch one at a bar. You don't have to find a shared interest to connect with others, you just have to share your interests. The rest will come naturally.
Ask for Introductions
If you happen to be with a buddy at an event and they have other people interacting with them, ask your buddy to make some introductions. This method of meeting people is a nice way for people at the shy end of the spectrum to meet new people. And your friends will understand.
Sometimes shy people have trouble networking because they don't think they have anything to offer, such as a job or a contact, to give back to someone who helped them. Although networking works best when you do have something to offer, what you offer doesn't have to be a job. Sincere interest in the other person—even flattery—is a form of generosity and goes a long way when you're networking. Be authentic, share your passions and let them feel good / successful about themselves.
If you are afraid of freezing up or getting tongue-tied in a social setting, prepare yourself in advance. Think of ice-breaker questions you can ask people you meet. If you're attending an event specifically to network your way to a new job, have your personal pitch ready.
Share your information—whether a website, article, report or phone number. This will build your credibility. If you promised to e-mail a contact / website to someone you met on the plane, make sure you do that. This will give the other person the impression that you keep your word. If you don't, you're just another schmoozer.
When you overcome your fear of rejection, it'll be easier to make cold calls and strike up conversations with strangers. The person sitting next to you at your local Wyndham Street bar after work may be feeling as uncomfortable as you are and will most likely appreciate you breaking the ice and saying hello. You never know, they just might be a fabulous contact for you or know the right person for you to talk to, but you will never know unless you try.