How I did it:
I moved to New York City, and live far enough away from my office that the only practical form of transportation to and from work every day is the subway. After a few weeks of completely-freaked-out riding, I started to relax and get used to just another everyday occurrence.
Resources:
http://www.mta.info/
It took me 1 month. It made me confident.
See more progress on Learn Not to Fear the Subway
See more progress on Learn Not to Fear the Subway
First published at 43Things