My current favorite blog post on networking (in the Harvard Business Review) says:
-Don't misunderstand the peeking order
-Don't ask to receive before you give
-Don't fail to state your value proposition
I would add:
-They have the power, they have the job; what can I give?
-Provide Information. You have done some research and you have been talking to people in this field. Everyone is trying to stay current, but no feels like they are completely up-to-date. (" ... I've been talking to execs in your market..." "....Recently I read...")
-Listen to their story. Everyone has one and most people want to tell it. Often the best favor you can provide someone is asking a few leading questions and letting them tell their story. ("... Wow, that must have been an interesting few years at ...").
-Why are they doing this? (Make it easy for them to help you.)
People take networking meetings or calls often because they want to feel like they are being a good person and helping others (and so that you can maybe help them later). So make it easy for them to help you.
-Ask for their advice. Reiterate it back to them in your thank you note and in the note you send them after you land a new job (in which you thank them again). This reinforces that they were helpful.
-Ask for a few (just a few) introductions. Crosscheck your target list with their LinkedIn contacts. (Use this list of company lists to create your target list.) LinkedIn makes this easy by providing a search box on the top of a person's contact list. (In that search box just type "Company A OR Company B OR Company C".)