Get good at small talk. Think in advance of a few questions that you could fire out at the person you are speaking with. When things start to stall out, be comfortable with moving on. Use geography, people in common, music, professional interests and anything else including the kitchen sink to build a bond with the person you are chatting with. If this is someone that you want to follow up with, make a note to send an email within a day or so. Better yet, write a hand-written note and actually put it in the mail. Yes, people still use snail mail and it's quite effective with networking follow up.
Don't just be influential, be influence-able. I learned early on in my education career that the following holds true, "No one cares how much you know until they know how much you care." While it's perfectly normal to want to 'get somewhere' in a networking conversation, you should also ask a few questions and show genuine interest in the other person. Don't settle for surface stuff, go deeper and show them that you care.
Balance your skills at advocating your position with your exquisite inquiry skills. The best networkers do their homework and meet people on purpose. As Keith Ferrazzi writes in Never Eat Alone, "the value of your networth is ultimately the depth of your network." I will be attending a national conference this week in Baltimore and I've looked at the list of presenters in advance- who do I want to stumble into'? Who is lunch-able? What unique way can I follow up with the guy I just met twenty minutes ago who might get me a job in five years?
On a personal note, I work primarily with students and their parents. It wasn't until I started looking at my job in terms of networking that the light bulb went off. Now, when I'm in small talk or sending an email or chatting on the phone, I am in networking mode and instead of one light bulb, it's more like a lit Christmas tree of ideas, all firing in succession and leading to future success.
Question: what can you to today to improve your networking skills?