Tailing is the practice of moving a venomous snake with a barehanded grip on its tail, generally with the aid of a hook or other tool to help control, support and direct the head. Some people use the term exclusively to mean gripping the snake by the tail with no other tools, but here we are referring to the safer practice of using a hook as well as a tail grip. Gravity is used to the handler's advantage, the hand controlling the tail held high enough that the snake should have difficulty launching an effective strike. The hook helps to support the snake's weight and also to control and direct its movements.
Regardless of the method, tailing is an advanced technique that is potentially risky. The strike range of some snakes is quite impressive even when they are being held at a very steep angle. Bitis in particular (Gaboons, rhinos and puffs) are capable of extremely high strikes and should never be "free tailed" without a hook angled over the neck to block a sudden upwards move. Smaller and lighter bodied snakes can also launch a strike well past their own tails regardless of the angle they are held at.
Mardi Snipes of Coastal Reptiles demonstrates his tailing technique with a large captive raised canebrake rattlesnake (Crotalus horridus, formerly h. atricaudatus). Note that his grip is slightly higher than the cloaca, and he is using his entire hand rather than just his thumb and forefinger to better support the weight of this exceptional specimen. The snake's considerable body weight is also being partially supported by the hook.
This animal is heavy enough that being lifted with a standard hook alone would probably cause it physical discomfort and might even cause real damage. Broken ribs are a fairly common finding on veterinary exams of large, heavy bodied snakes that have been repeatedly lifted with hooks. The more comfortable and well supported an animal is during the handling, the less likely it is to struggle, which is safer for both snake and handler. You may wish to consider safer alternatives to tailing a snake that is already agitated and showing extreme defensive behavior, such as tubing, tongs or a Pro Bagger.
Ideally a snake is tailed only long enough to move it safely during necessary husbandry routines. There is potential for injury to both snake and handler if an animal becomes uncomfortable or agitated while you are tailing it. In particular it is very easy to accidentally drop a rattlesnake's rattle during this procedure if it takes you by surprise and pulls its tail too quickly through your hand. You can sometimes pop the dropped segments back on, but it's better to avoid this in the first place and keep your tailing time to the minimum necessary to safely move the animal.
Elapids are physically and behaviorally different from pit vipers, and require slightly different tailing techniques.