Google League of American Bicyclists and see if they're offering any bicycle education and safety classes in your area. They're just what you're looking for.
Beyond that, it primarily takes practice. I started off by riding on country roads with little traffic and that got me used to being on the road. Bike handling is certainly part of the equation. You need to be able to ride a steady line and to look behind you without veering all over the place. Well-placed mirrors can help with that, although I don't ride with one myself. Learning out to ride defensively in traffic is also part of it. That's not all that different from driving in a car. You have to be watchful at all times. Knowing the rules of the road as they pertain to cyclists also helps, as does wearing high viz clothing and using a good taillight (and other lights if necessary) is also helpful.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher