Horcrux

To create a, or multiple, horcrux(es), you need to kill someone. Not for self-defence, or to protect someone else, or for any other good intention, but just for the sake of killing someone. It's supposed to be an act of pure evil, make sure it is. After you killed the person, you can have no regret or remorse, or it won't work. To create a horcrux, what is considered the worst of all Dark Arts, you have to be evil. If you're not, there's simply no chance for you to create it.

After you killed the person, any way is acceptable as long as the person ends up dead, your soul is torn apart into pieces. Then you can cast a spell to encase the damaged piece of your soul into an object, animate or inanimate. You'd want to make it an inanimate object, since it's harder to destroy. As long as the horcrux, a.k.a. the object is intact, a piece of your soul is too, making you immortal.

It was believed for long that one can create only one horcrux, a.k.a. tear ones soul only one time. But after Voldemort decided that in theory, creating multiple one would work. He created seven horcruxes. Even tho only creating one horcrux destroys your soul and makes it unstable, creating more than seven has never been tried but is highly believed to be deadly. Voldemorts soul was so unstable and fragile that his soul could be easily tampered with, if you got close enough.

After creating a horcrux, you want to make sure that it will not be destroyed. So you should put multiple protection charms on it, and hide it well or always keep it with you. Make sure that no one, not even your closest family, friends or partner knows that you have a horcrux, and even more important that they don't know what object it is. Even if they'd never purposely tell anyone, they might be tortured or someone might steal their memories. Keep this to yourself, and yourself only. You'll either want to hide the horcrux in a very safe, obscure place like at the bottom of a deep sea (in that case, rememebr to make sure there's nothing at the bottom that could destroy it). Or, you could try hiding it in plain sight. If your horcrux is a piece of jewlery that's been in your family for generations, you might want to hide it away well, since it's the first thing people will suspect is your horcrux. However if your horcrux is something uselss, like a brick, it'll take the person who knows you deepest and is very intelligent to figure it out. So this horcrux you can hide in plain sight. In a random brick house's backyard, just make sure that it's in a calm neighbour hood and in a place where it's least likely to come natural disasters or some human caused problems.

Now onto the incantation. Canonically, it's unknown. So if you follow the canon to 100%, you won't be able to create a horcrux. But personally, I wanted this information to exist somewhere, so I went ahead and made up the spell (Just to clarify, the incantation is NOT canon, it's just my own headcanon that I choose to use. I'd love if you used it too and made it a 'thing').

The incantation is Incapsa Anima. In means in (simple). Capsa is a Latin word for case or box, so when put together they become in-box, or, encase. Anima is the Latin word for soul, so the incantations direct translation would be Encase Soul.

Your concentration does not need to be high for this spell, simply concentrate on the object and set your intention, point your wand directly at it and say the incantation. Your willpower however, needs to be really high. This is something an ordinary witch or wizard can not do. Your experience with magic, spells and especially Dark Arts has to be alot. Imagine putting a piece of your soul into an object - I think you can see why it needs high willpower.