I just learned how to ride a bike 6 months ago (I'm 31). My very patient boyfriend took me to a LBS, where someone from the shop and my bf taught me in about an hour. I would definitely recommend going to an LBS since they probably have experience teaching very afraid people to ride.
I started on a MTB with a very low seat. First I just pushed myself along to get used to the bike, then coasted down a very gentle slope, and practiced braking. Eventually I started pedaling slowly with my bf holding onto the handlebars. When I was confident enough he stopped holding the bike and I began riding on my own.
It took a few months for me to get used to traffic, but now I bike 100-150 miles a week!