Networking without feeling pushy after 13 years as a marketing coordinator

A friend suggested informational chats and I do not know how to ask. Some people reply with short answers. How do you phrase the request?

Thanks for writing this out. I went through something close to it last year, and it settled down once I kept a simple log of every call and form.

Follow up with a thank-you and a short update. One of my chats led to a referral a month later.