It's quite simple actually. Simply purchase a roll of deer netting. The last one I bought was only $10. It only took 1 roll to cover 2 runs. I unrolled the netting and secured it to the fence all around the run with zip ties. I place the zip ties about every foot along the top of the fence. You can place them closer though if you want. If your coop is central to the run you can just drape it over the top. You may have to prop the netting up in the middle if you have a huge run. In the grow out pen I simply added an extra tall fence post and secured the netting to it. This keeps if from hanging down in the middle. I also cut small slits in the netting for the fence poles to come through.
Now keep in mind that this only helps to keep out birds like hawks. They see the netting and usually don't even try to get through it. It's a visual deterrent more then a physical deterrent. Obviously other predators can rip through it if they try. I'm sure a hawk could rip through it if it tried too. Most simply wont try. We did this for the first time about 4 years ago when we had a turkey vulture attack our call ducks. We haven't had a problem in that pen since however the uncovered pen has had 2 hawk attacks. Interesting thought isn't it? The pens are across the yard from each other.....approximately a football fields length apart. Such a simple and cheap method to protect from aerial attacks.
Of course the safest method is to always supervise your chickens when they're outside...however, this is a good deterrent for those times when you simply can't be there.