With their talons.
Talons are the claws on birds of prey and one of the two body parts that identify them as raptors, the other being their sharp beaks.
On peregrines, the talons are especially long and deadly.
The photo at left shows a peregrine's feet on a rehabber's glove with one talon circled in green. See how long and curved that talon is? About 3/4" long. Nearly as long as the first joint of the rehabber's finger.
And whose talon is this?
Click on the photo to see PittStop, a female peregrine born at the Gulf Tower in 2003 who injured her wing when she hit a building that July. She was taken to Medina Raptor Center in Spencer, Ohio and underwent flight training in the spring of 2004 to regain her wing strength after her initial injury healed. That's when this photo was taken.
Unfortunately Pittstop's injury was too extensive. Her wing always droops, she cannot fly well enough to hunt, and she sometimes has damage-related seizures.
(photo by Chad+Chris Saladin, altered to illustrate the feet and talons)