The Tire Drag obstacle is one of those simple (to explain), there isn't a lot to say regarding specifics techniques or tips.
First, you have to pick up the tire and take it far away until the rope is fully extended. Return to the rope attachment point, sit down, the butt must be on the ground, grab the rope and start to drag the tire.
In some events order may be reversed, (pulling first, followed by dragging).
That's it, what you need here is pure strength, both in legs and arms muscles.
In the below video tutorial you can see the girl that complete this obstacle perfectly. Follow her movements and train to add strength where you need it!