Find a large empty parking lot and practice just driving the car - get used to maneuvering it, accelerating, stopping suddenly, driving backwards, etc. - take some cones or empty cardboard boxes with you to practice parallel parking or other maneuvers.
When you are more comfortable with the car itself - and know how it will react in various situations, then you will have more confidence in your ability to drive on the road - but don't get too cocky. Some of the biggest problems you will face is distracted and/or incompetent drivers, aggressive drivers, and road conditions (road work, inclement weather, etc).
While you are getting used to driving, avoid high-traffic places and times of day - eventually you will be able to handle yourself in a variety of situations.
Make sure to keep your car in good functioning conditions - good tires, brakes, etc. are essentials, but also regular oil changes, filters, and other things to keep your vehicle tuned up.