The easiest way, though it is a long drive, is to take your car. That way you get to enjoy the many places worth a stop along the road. You also need a car when you get to Charleville so that you can experience the outback, and perhaps venture on to more outback towns.
However there are other ways to arrive:
Air: Qantas has freuqent flights. www.qantas.com
Rail: ww.traveltrain.com.au Trains twice a week.
Coach: Greyhound Coach www.greyhound.com.au Coaches daily.
You can also hire a vehicle when in the area - but advance booking is advised.
Be sure that your vehicle is equipped with bull bars, so that if (when) you encounter a live (or freshly dead) 'roo in the middle of the road, you don't wind up making a claim on your auto insurance.
Failing that, try to get behind someone who is so equipped -- but still keep a sharp eye out for the jumpy buggers.
If you do hit a 'roo, it's just good manners to stop and get the carcass out of the road, so that the next traveller doesn't have to dodge off into the ditch to avoid your handiwork.
Drive during the day, and avoid being on the roads at dusk or during the night. Over about a week of Outback driving, following this simple guideline, we only saw about a half-dozen different 'roos. Live, that is. Hundreds - no, thousands - of retired 'roos, but not too many live ones.
Still, keep your eyes peeled; 'roos are pretty unpredictable, and they can easily jump right into the path of your vehicle, even if they seem to be impossibly far off to the side of the road as you approach.