Most of the equipment we use with raptors is the same stuff used by falconers for hundreds of years.
In falconry, as in many specialized disciplines, they have a peculiar name for everything, thus when a bird poops it is called "muting," and when it is panting, it's called "gular fluttering," ad infinitum.
To prepare a bird for perching "on the fist," you must get leather "bracelets" on their legs. The bracelets have grommets, through which you string the "jesses" - leather strips about the length of the bird's legs. The jesses are threaded through a metal "swivel" that has a ring on each end. Finally, you can thread a "leash" through the bottom ring of the swivel.
We practice the "falconer's knot" (also known to equestrians), which you can tie with one hand and secure a bird to a perch, but you can quickly release it.
We wear a welding glove on the left hand. The birds in the mews already have bracelets and jesses, and are well-trained to the fist, so we go in for Cocomo (a beatiful male dark-morph red-tailed hawk), and get him off his perch. This involves approaching him carefully, grabbing the jesses and getting them into your palm with tuhmb and forefingers holding it secure while he perches on your hand. Then you thread the pair of jesses through the top ring of the swivel, and thread the bottom ring of the swivel thru slits in the ends of the paired jesses. Then you slip the leash from around your neck and thread it through the bottom ring of the swivel (it has a "button" at the far end to prevent it slipping all the way through). Then, you get the swivel between the two pairs of fingers on your gloved hand, and loop the extra leash around the pinkie. All this while keeping your hand as still as possible, in a fist, with the bird perched on the "platform" provided by the flat of your thumb and forefinger in your vertical fist. Cocomo is a sweetheart - an amazingly patient bird, though he looks at me sometimes like "what the hell do you think you're doing?" He has a problem with his pelvis, so once in hand he generally has a wide stance and holds his tail flat against the back of your fist.
Hawks will occasionally "bate," trying to fly away while you have them in hand. They end up upside-down, and sometimes twisting around. You have to keep the "platform" of your fist relatively parallel to the bird's feet, and sometimes you have to get your right hand under them and lift them back up. Ideally, if you provide a still, solid, flat perch for them, they don't do this - much - but it's a real pain and quite stressful to me when they do.
We learn how to get Cocomo onto the bow perch (a half-circle about 10" high covered with astroturf) and tie the flaconer's knot with him actually on the other end of the leash. Once he is tied thus to the perch, he can be left there secure.
Next, we go to do the same with "Knuckles," a one-winged great horned owl. Knuckles is aptly named. Thru the whole process described above (and *I* am volunteered for this one), he resists any appearance of cooperation. When I go to get him off the perch, he flutters to the floor and I chase him from one corner to another of the mew, kneeing around in the wet pea-gravel, before I finally manage to grab the jesses and get him on my fist. Now, while I attempt to get the jesses lined up and the swivel on, he is seeking to bite the fingers of my ungloved right hand whenever he can, and he does manage to knick one of my knuckles just a bit. Meanwhile, he clamps onto my gloved hand with his talons and it's like a steel vice - just amazingly powerful, that grip - and he occasionally gets a good piece of gloved thumb in his beak as well. It would NOT do to get this attention on unprotected flesh and bone.
After an eternity, I have him in hand with jesses, swivel, and leash all in place. I am delighted to transfer the little bastard to one of the other trainees, but I also keep in mind that the difficult birds make you appreciate the "easy" birds more, and when you can handle the tough ones, you can handle all of them. All three of us get a good amount of time with the birds outside, holding them, perching them, unperching them, transferring them.
It is still exciting and a little unnerving to have one of these guys perched on my fist and staring at me. I feel inconsequential in their eyes - not unlike the way you might feel sometimes with your cat, knowing that if it wanted, it could do some serious damage... Still, I love these birds, and it is a rare privilege to be allowed this close, and maybe to develop the same kind of relationship I have with the cat.