Apologizing merely demonstrates your lack of professionalism and confidence. It's also annoying and juvenile. 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 her out.

Tap into Your Primal Instincts

"Humans are hard-wired as communal, tribal animals, so the shy person isn't shy by nature," says Ferrazzi. "They are shy by design. Something happened to them to make them want to recoil."

Sometimes, when an introvert hears that he's not inherently a loner, that humans are innately social creatures, the realization helps him emerge from his shell of shyness, he says.

Be Yourself

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 gregarious than normal, you shouldn't be artificial.

"You don't have to be the schmoozer," says Never Eat Alone's Ferrazzi. The problem with the schmoozer's approach to networking is that he doesn't have the right intent: He's not interested in helping other people — only himself, says Ferrazzi.

"Be the authentic, aw-shucks, humble, shy person you are. It can be endearing. Don't try to be something you're not," adds Ferrazzi.

In other words, it's OK if you're a little awkward. Just don't keep apologizing for it.

Tap into Your Passions

Sarikas recommends joining clubs and attending events that relate to an interest or activity you enjoy. If you're a budding oenophile, attend a wine tasting at your local liquor store. Eager reader? Join a book club. Can't get enough of the pigskin? Attend a football game or watch one at a bar.

"Just because you're a technology professional doesn't mean you should only go to technology conferences to network," says Sarikas. "That person sitting in front of you [at the ball game] might have a job you always dreamed about or work in a company that you want to get into. You could sit behind them the whole season and never know that unless you initiate a conversation."

The advantage of engaging in activities you enjoy with other people is that it makes conversation so much easier. So while you're analyzing the cabernet's nose, discussing the plot of A Thousand Splendid Suns or sharing game stats, ask the person with whom you're chatting for her name and about her work. There's no reason not to do so if you're having an amiable conversation.