Any tips for an introvert to network in a professional setting?

Hey guys, I'm new to this subreddit. I came here after watching Susan Cain's TedX video, and I've read her book years ago.

There's a long background story but I'll try and summarize as much as I can:

I just moved to NYC and got married to my husband to bring our long distance relationship to a close (ever since DOMA was ruled unconstitutional two years ago that made this possible—we're gay). I was a writer / editor in my home country, and continued to work remotely / do some freelance writing gigs until recently over the new year, I decided that I needed a career change. My job hunting in the US to be a writer / editor has gone nowhere.

I decided I wanted to look into being a financial planner (having graduated with a degree in Econs & Finance) as personal finance is one of my other passions in life. I started to enroll in a Certificate in Financial Planning course even though this means I'm hemorrhaging money while being unemployed, and I started to volunteer to help low-income taxpayers to prepare their tax returns.

All that I've been reading so far though is that to get a foot in the industry (which in my mind is getting an entry-level financial planning position at a small boutique fee-only firm, so as to avoid the terrifying salesman jobs), I have to network network network. Quite possibly the word I'm absolutely mortified with.

I'm looking to attend a financial planning association locally to network, and if there's one thing I realized about myself these days, it's that I'm horrible at small talk. Even when I was at a tax prep site preparing taxes, my conversation with the taxpayers are limited to "business" questions (ie: only relevant questions related to their taxes), where else some of my colleagues made jokes, laughed, asked the right questions that elicit friendly reactions from the taxpayers. I'm terrible at making jokes—especially with a stranger—so that's something I'm unlikely to do.

I think there's also a cultural gap which I'll have to learn to close, but in summary, my questions are:

1) How do I network in a professional setting? I'm forcing myself to get out of my comfort zone to attend some networking sessions in order to hopefully get my foot in the industry.

2) How do I get better at small talk? Would you guys have any tips?