First, decide whether this animal should be lifted at all
Carrying is for kids, lambs and genuinely small animals. A fit adult sheep or goat is heavy, strong and awkward, and trying to carry one risks a dropped animal, a kicked handler, or both — adults should be walked up a ramp, led with a halter, or moved in a crate on a trolley. Even with youngsters, if the animal is fighting hard or the ground is muddy and steep, the safe answer is to change the setup: bring the vehicle closer, use a low trailer, or pen the animal where it can be loaded at ground level.
Young orphans and poorly youngsters are the exception that proves the rule — they are exactly the animals that do get carried, to the vet, to a foster pen, into the warm — and they are fragile, so the hold matters.
The supported hold for a kid or lamb
Crouch beside the animal rather than bending over it, and let it settle for a moment with a hand resting on its back. Slide one arm under its chest, just behind the front legs, and the other arm under its hindquarters so the rear end is cupped and supported. Lift with your legs, bringing the animal snug in against your body, one hand still under the chest and the other keeping the hindquarters tucked so the lamb or kid feels held on all sides.
Held this way, most youngsters relax within seconds, because nothing dangles and nothing is gripped hard. Keep the head free and uncovered, and talk to it as you move. Never lift by a single leg, which can damage a shoulder or hip joint; never by the ears or scruff; and never, with a lamb, by a handful of wool — it tears the skin away from the muscle underneath and bruises badly, quite apart from hurting. A sheep of any size that must be handled should be tipped and held by a handler who knows how, not scooped up by its fleece.
The carry to the vehicle, and the step up
Walk slowly and watch your footing — most carrying accidents are the carrier tripping, not the animal escaping. Have the crate or pen inside the vehicle already open and bedded before you pick the animal up, so you are not fumbling with a latch one-handed while holding a wriggling kid. If the step up is high, reverse the order: step up backwards so you can see where your feet are going, or hand the animal to a helper standing in the vehicle while you keep both hands on it until they have it.
Set the youngster down gently into the bedding, hindquarters first then chest, and keep a hand on it for a moment until it finds its feet and realises it can stand. Close the crate before you let go completely — a kid that has been calm in your arms can still make a sudden bid for freedom at the sight of daylight.
Afterwards, and the human half of the job
Watch the animal for a minute once it is loaded: it should stand, look around, and settle. A youngster that lies flat, cries continuously or has laboured breathing after an ordinary carry needs a closer look and possibly a vet call before any journey. Check yourself, too — wash your hands and any scratches, and be honest about your back: a half-grown lamb is a respectable weight, and lifting several in a row is a job for two people or a ramp.
If helpers or a sitter ever load youngsters for you, the hold is worth writing down rather than describing once in the yard: a KinsLe Care Pass lets you leave the handling notes — the supported hold, what never to lift by, which animals are carried and which are walked — where the person doing the job can actually read them.