Handling an owl, obviously, is not something that you can or should just go out and do on your own. With that in mind, consider this instructable as a general overview of what you are getting yourself into if you decide to do this with supervision. A good place to do this would be a zoo or a state park that takes in wounded animals. I learned from a ranger at Natchez Trace State Park in Tennessee. Do not attempt to do this with a wild bird, as it may be illegal and endanger you or the animal.
Step 1: Get Ready
Before handling any bird of prey, make sure you have a set of thick gloves, otherwise their talons can injure you, and the bigger the bird the greater the injury, no matter how careful you are. You should also have a leash with two hooks--one for each ankle--in order to prevent the bird from flying off of your arm.
Make sure to put on the leash before you put on the gloves, so that the leash will be a bit snugger on your wrist.
Step 2: Hook the Owl to the Leash
To hook the owl to the leash, put your gloved arm next to its perch and allow it to climb onto your arm. From there, grip its legs quickly and turn it upside down, attaching a hook to each ankle. Grip the leash close to the hooks and allow the owl to correct itself on your arm.
Step 3: Putting the Owl Back in Its Cage
You've done it! The owl is officially on your arm! To get it off, simply unhook the owl and throw it back in its cage using a soft underhand toss, away from any obstacles.