Of course, every situation is different but this template can help you get the most of such meetings:
Phone or skype meetings are okay but in-person, if feasible, may be worth the effort.
Mirror the person. Dress as s/he does. Begin the meeting with the amount and type of small-talk that works best for them. Your utterances should be at their speed, average length, intensity, intellectual level and emotional level.
When it's time to get down to business, ask whether s/he prefers you ask questions to identify if and how you might be helpful to them, or whether she/d prefer you describe how you present yourself to the job market and show your resume so s/he can provide feedback. Respond accordingly. If the person offers a suggestion, try if possible, to simply say thank you and not argue.
At the moment it feels right, ask if s/he knows someone you should talk with, something you should read, a meeting, conference or other event you should attend. When they offer one, ask, "Great. By any chance, do you have another idea?"
End by asking, "Would you mind keeping your ears open for me and if, in a month, I'm still looking, I follow up with you?" The person will usually say yes, which means you've recruited a scout, someone who'll keep the antennae out for you. The person is likely to have more leads for you during the month than what s/he has at the moment you're asking .
After the interview, write, not a thank-you note, but an influencing letter. After the obligatory "Thanks for meeting with me," that letter should include as many of these as is appropriate:
- Say you appreciate that he was impressed with (insert the thing he was most impressed with about you.)
- If you flubbed something in the meeting, write, "I've given further thought to your question about X. (insert improved answer.)
- If you've identified a way in which you might be of help to the person---a project you could do, or even a full-time job--append a half-to-one-page proposal.
- Thank the person for offering to keep her ears open and willingness to take your call if, in a month, you're still looking.
After the meeting it's often a good idea to send a personalized small thank-you gift. For example, if he mentioned that he's about to buy a new car--I'd buy him a book on the art of buying a new car. I usually buy such presents from convenient Amazon.
That approach should generate benefit in excess of the time you spend obtaining and attending such meetings. If your meetings routinely yield little benefit, you're probably talking too much, listening too poorly, not showing interest in them, and/or shooting for a too low-probability job target.