Prepare yourself. Find out about the event, the venue, look at photos from previous events.
Reach out. Say hello.
Small talk. Try to understand who the other person is. Ask polite, open-ended, questions. Listen a lot. Show positive attention.
If the other person asks you questions back you can move forward and ask some more detailed questions and share some more personal thoughts. Now you are moving towards creating a relationship of some sorts, a very thin relationship but nevertheless a relationship.
When it is time to move on or home you can ask the person for his or her contact details.
If you have mingled around and talked with other people before you leave the event you should return to persons you have had a good talk with and say a proper good bye.
Within a few days you should reconnect. Send the person a short message and thank him for the good conversation and say you look forward to talking again in the near future. Sending this short message reinforce the memory of you with the other person and strengthen your initial bond.
Follow up again. Send short news summaries, post online.
Always connect with the host of networking events, she knows more persons than anybody else.
Add value. Share things that might be positive for others. Make introductions. Be useful to others at events.