First, read the book The Fine Art of Small Talk. It's a quick read and inside is a list of Do's and Don'ts. I wrote down the list and have a printed sheet in my car. Each time I arrive at a networking event, I review the sheet and think of topics. My full review is here.
For me, it becomes a game: Using my learned small talk skills I try to figure out ways to help people. Sometimes it's information, sometimes it's a connection. Besides being fun, it's feels great to help people. What's also happening is I'm becoming valuable to them and they will want to connect with me. It really is all about yo mindset and using some simple learned communication skills.
When you meet someone who you like and/or you think you can help, follow up with them. Do it that evening - don't wait. In the follow-up make sure to at least include 3 things:
- Thank them for the conversation about __________________ (you might need to take notes during the event so you can remind them what you talked about - they won't remember. I write on the card they hand me).
- Invite them to connect again, either over the phone or in person, for a specific purpose (probably related to what you talked about).
- Add your picture at the bottom of the message (just to doubly make sure they remember who you are).
Again, implied in those 3 points is that while networking, seek ways to help others. Also, since this requires you to have a real conversation and real follow-up, don't go over board. I'm usually only capable of really connecting with 3-5 people at a networking event. I do usually walk away with 20+ cards, but only a handful are actually meaningful to me.
I suppose you could send everyone you meet a LinkedIn invitation reminding them of where you met. That way you at least keep that "connection". But, I don't know... I've never done that before... but I tend to be more selective about who I connect with (not sure if that's good or bad). Plus, you creep dangerously close to being "that person" at the networking event.
Again, it's not about the quantity, but about the quality. If you genuinely help a few people, word will get around to many people that you're a person worth connecting with.
Two other books I read which helped me are Never Eat Alone (my review) and Endless Referrals.