Networking without feeling pushy - any advice?

A friend suggested informational chats and I do not know how to ask. I worry about bothering people. Did any turn into leads?

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

Thanks for writing this out. I went through something close to it 5 months ago, and it got easier once I kept a simple log of every call and form.