If you have an electric awning, you don't want to tie it down. If it gets 'that' windy, roll it up.
If you have a manual operated awning, you got a couple options. 1) Roll it up, or 2) tie it down. However, if the wind becomes too strong, you want to roll it up regardless.
But for moderate wind, air movement, to keep it from flapping, there's several ways to do it. The thing you do not want to do is anchor the awning down solid with ropes directly to a tree or to a tent stake. You need some kind of flexibility in the line which will prevent you from over tightening the line and potentially bending your awning arms.
Here's a very easy and inexpensive way to do it. Get a couple dog screw anchors that you'd leash a dog to:
Screw these in the ground about 5-10 feet out from your extended awning. Then use a bungie cord on each anchor (to act as a spring), and then tie a rope around the awning roller arm and catch it with the other end of the bungie cord. You do not want to draw the bungie cord tight, just nice and springy.
All you are doing is keeping the awning from flipping over the top of the trailer in the event of a huge wind gust. The bungie cord 'spring' will allow the camper to shake and wiggle in the wind without stressing the awning arms being anchored to something fixed. Also, will prevent you from over tightening the rope (or if you perfer, use a ratchet strap).
The reason you do not want to tie down an electric awning, is because they are spring loaded, and actually made to move in the wind, and self-tilt if they pool with rain water.