There are books, blogs any number of resources out there to tell you how to be a better networker. None of those networking techniques will mean much unless you follow up in a timely manner with the people you meet.
There’s really no correct way to follow up. E-mail, phone call, snail mail, tweet, text, you name it. What does matter is conducting that follow-up in a timely manner. The typical guideline for follow-up is within two business days.
While timeliness is a key component, so is what you say. “A nice meeting you” note is fine, but will it leave much of an impression? Probably not.
In your follow-up, mention a topic you discussed with the person. If you talked about their business and some particular issue they were having, reference that. You don’t necessarily need to solve the problem but it’s important to get across that you were listening and took somewhat of an interest. The very last thing you want to do is follow up and have the person on the receiving end feel like you only followed up because you want their business.
One easy, unforced way to follow up with people you meet at a networking event is to ask if it’s okay to put them on your mailing list (if you have a company newsletter). This accomplishes a couple of things. First, it’s a fairly easy thing to do (e.g. “it was nice meeting you at the ___, would you mind terribly if I put you on our mailing list so we can keep in touch). Second, it shows consideration of their needs and not wanting to add yet another unwanted e-mail to their inbox. Nine times out of 10, they will respond favorably to that kind of request and your connection is now made.