If the person does not reply/reach out to you, I would give it a couple of days and then send a polite note asking if he/she will pass your resume along to the person doing the hiring or if he/she would be willing to meet with you for an informational interview so that you could learn more about the organization.
If the latter, then, when you apply for the job, put a note in your cover letter that you enjoyed meeting so-and-so and learning more about the organization from them. That way, the person doing the hiring will likely contact the person to ask them about you.