The best way to get to the Volcano area is via car. There may be shuttle buses, but they would be few and far between. The only other way is via tour bus from either Hilo or Kona, but you're stuck with their schedule and you have to leave when they want to.
You will need a car to drive around and see everything. You can hike around if you're fit, but the road down to the ocean is several miles long (about 20 miles?) so it would be quite a hike.