Okay... How do you sprawl? Since the thread is "Back to Basics" I'll offer you a few tidbits that are readily applicable even before you get to where you have to sprawl. All these little bits make a difference in defending takedowns, whether they be double-leg, single-leg or greco-roman style take downs.
All leg dives and shots can be broken down and explained like this: You take your opponent down by restricting the movement of their base while destroying their center of gravity. Restricting the movement of your opponent's base is down by grabbing ahold of the person's leg(s), isolating/controlling it and then bringing it out from under their center of gravity/hips by pushing, pulling or lifting. Sounds a little too simplified, right? It is, but when the concept of the technique is understood the principles of defending it become clear.
First rule of defending a shot: Control distance and range. Just like any punch or kick, it doesn't do any good to shoot from too far away. So how do you know when you are in shooting range? The general rule of thumb is if you can touch your opponent, you can shoot on them. This is the reason why you see grapplers tap their opponent's on the head, chest or shoulder. Not only does it distract the person, it also acts as a range finder. In MMA, you would use the jab. Once you can connect solidly, you can shoot effectively. The flip side of that is that they can shoot on you too. By controlling distance and range with footwork and mobility, you afford yourself that extra 100th of a second to setup or defend a shot.
Second rule of defending a shot: Keep on the same level (or lower) than your opponent. Just as a good shooter will drop their level before they shoot, you should drop your level to match their's to defend the shot. Remember, in order to destroy your center of gravity they have get underneath it. Dropping your level to match theirs will put your body in a solid position right in front of theirs. This is also the reason why a lot of guys miss sinking in underhooks when someone shoots on them. Their upperbody is still completely upright while their opponent is knee-level diving for their legs.
Third rule or defending a shot: Do not fight their force head on, redirect it. Just like you don't want to back up straight in a striking contest, you don't want to end up in a test of strength during a takedown if you can avoid it. When you are in a crash position, head-to-head, chest-to-chest with an opponent driving into you, realize that trying to muscle through them is a waste of energy (even if you are stronger than them). It is best to redirect their energy and turn them to the side of you or straight down while you move away from their path. In fact, when you sprawl you are using your body and gravity to direct their shot and force directly into the ground underneath you.
Keep those in mind when you looking to shoot, or looking to defend a shot and picking up on specific techniques to implement during that time (like the sprawl) becomes an easier task. I'll tackle sprawling (no pun intended), if nobody covers it before me, when I come back from the dojo.
It doesn't matter if you agree or disagree
... As long as I don't bore you and I spark a moment of thought, my goal is achieved
Queng leon queng tigre ecu tacacut, queca pa? - Pampangan Mandarigma Motto