Go public places and start saying "hello" (only) to people; store clerks, librarians, waitpersons, park rangers :-)
You can network without networking, get to just talking to people about the weather and where you're going, where you been, etc. and things open up. Won't be fast or anything but people know people who know people, etc. I sold my old car on the bus one day because I was telling my seatmate the story of how I wanted to sell it but one guy wanted to use it as a funny car and I didn't want that for my baby of 12-13 years, LOL. That I "cared" about my car came through so a couple realized they could trust me about the car and came to see it, I let them take it to be looked at by a mechanic friend of theirs, etc.
I was offered a job by a woman in line with me at the library checkout desk. I knew the checkout clerk because I was at the library so much. Just go places you "enjoy" and be seen a lot and then slowly say "hi" to clerks you recognize, etc. Eventually you will be able to say a few words more or they'll greet you, etc. and it won't be and "equals"/specific topic conversation so you won't be as anxious.
Do you listen to motivational tapes at all (I use to buy an occasional book on tape to play in my car as I was driving to/from places) or read books on the subject? Keeping yourself immersed in ideas and thoughts might help get you to try some when you're not "thinking" about it? Just doing often works.
I recommend sales books by Zig Ziglar and Joe Girard.
Wishcraft by Barbara Sher
http://www.wishcraft.com/ (and her other books).
Start small and your anxiety won't be affected, go under its radar.