I'm happy to see some good responses and suggestions already.
Keep 'em coming! I hope this thread will be a resource for people who are beginning to experiment with becoming less reliant on cars.
One of the first things I had to learn was
how to ride a bike in traffic, and feel safe and comfortable doing it. There are a number of books and websites that helped me to learn this, as well as the Advocacy and Safety subforum here on BF. Politically speaking, I am not at all a VC person (vehicular cycling). But the VC people do have some good educational material on riding as a part of the traffic that I thought was helpful.
Another thing I learned early on was about
riding in darkness, and the importance of good lights. We're lucky these days that cheap bright lights are widely available, and don't require much special knowledge to purchase and use. If you're an active carfree cyclist, you might spend almost half of your riding time in darkness, especially in the winter time.
A third early lesson was about
route planning and trip planning. It's often better to take a different route than you would take when driving. Good resources are Google Maps, bike maps put out by local bike clubs, and above all, just exploring on my own.