This is the most crucial step. You've met them. You have their business card. Now what?
Start emailing.
Make sure you write unique emails for each person you're following up to and include a tidbit about who you are, how you two met and where as reminders. Same for if you send a LinkedIn request.
Keep the emails short and sweet and action-oriented. Do you want to meet for coffee? Do you want to show them your book? Let them know what you want to happen next at the end of the message.
I've written about this a lot, in much more detail, so here are links to get you going.
Email Dos & Don'ts
The Art of Emailing
I Won't Hire People Who Use Poor Grammar
How Formal Should Your Email Be?
Keep in Touch
7 Things You're Doing Wrong on Linkedin
How to Get Ignored on LinkedIn