3 answers
The best thing is to leave it alone. Hedgehogs are wild animals that usually pass through at night looking for insects and slugs, so it'll move on by itself. If you want to help, you can put out a bowl of fresh water in a quiet corner of the garden, away from dogs and cats. Avoid touching it or trying to pick it up unless it's visibly injured or in distress - hedgehogs curl into a ball when they're scared and can get stressed easily.
If the hedgehog seems to be suffering though (limping, not moving, covered in visible parasites), then yes, contact a local wildlife rescue center or a vet who works with wild animals. In the meantime you can gently isolate it in a box with towels, in the dark and warmth, and offer it some water. Don't give it milk - it's a myth that hedgehogs like it; actually, a lot of them are lactose intolerant.
As for your garden in general: if you want to attract hedgehogs (which is a good thing because they naturally control pests), leave some wild areas with piles of leaves and wood, reduce pesticide use, and make sure they have escape routes to other spaces. A hole in a hedge or fence makes it easier for them to move from one area to another.
Are you worried it might cause damage, or is it more out of curiosity?
Anyway, the good news is that hedgehogs are your allies. They won't ruin your plants or attack anything of value - quite the opposite: they eat slugs, insects, and larvae that could cause problems. If you find one, the simplest advice is to leave it alone. But if you want it to move on, create a way out for it, maybe by making a small gap under the fence. Hedgehogs move around at night, so you won't see them hanging around your garden all day.
If you notice it keeps coming back, check whether there's something attracting it: food left outside, stagnant water bowls, or piles of leaves where it might have made a den. If it really does become a problem (which is rare), avoid using pesticides because they're poisonous to them. A less invasive solution is simply to coexist with its presence, which honestly doesn't cause any real trouble. They're shy creatures and prefer to stay away from anything that distracts them.
A hedgehog passing through your garden is basically a gift: it eats slugs, insects and pests that would otherwise damage your plants. I've seen one a couple of times in the evening and I just let it do its rounds, and it went back on its own the night after - if you don't have poisons lying around or dangerous obstacles, there's nothing to worry about.
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