Who is the chairperson of your local Democratic Committee?
You should be able to do a quick search to find out. (You may have found it on Day 1 when your thing was to find out about the next meeting.)
Once you have the Chairperson’s name, see if you can connect on LinkedIn, Twitter or Facebook. Email a few friend who might be 1 or 2 degrees of separation and see if you can set up a meeting. Or just an email exchange telling the chairperson that you’d like to become involved.
I did this, and it took less than 15 minutes. (Of course, then I got nosy and Google Earth-ed the office, etc., so my actual time was a bit longer….)