Lots of people have a hard time asking for what they want; they do not want to be pesty or they think they do not deserve it. Do yourself a BIG favor and flip it around. Do not think in terms of connecting with people to get what you want; think about how YOU can help THEM.
Everyone thinks about financial equity, but building emotional equity is so much more valuable and satisfying. The more you help people get what they want, the more they'll help you. When you're networking, you're not just looking blindly for people who can give you stuff; you're looking to create another kind of family-people you care about, people who will care about you. Follow your intuition; it'll tell you whom to approach and how. Look for people to connect to, to develop relationships with. In the end, it's those relationships that matter, that will make the journey worthwhile.
Do not approach others with an open hand-that "lean and hungry look" oozes desperation. Have you ever noticed there's a physicality to the gimme? There's a way people look at you when they want something: eager, impatient, and expectant. Sometimes they are leaning forward, as if preparing to grab. They're watching for their moment, and if they do not get it, their disappointment is reflected all over their face. Relax, kick back in your mind, and just try to get to know the people you're talking to. Ask them about their business, their ideal customer, and their goals. Ask what they do for fun, find out what they care about. People have fascinating lives, businesses, challenges, and triumphs. Seek out these stories and you'll gain valuable insights and maybe even lessons.