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Press "E" when the item is adjacent to you and then press "Wield in left/right hand", if you press "?" or "help" in the pause menu it will show you a list of key bindings :)

Yes I saw all that, I was expecting a way to put things in my inventory...

You don't have an Inventory like in most games, instead you can find all types of carrying containers like backpacks and shoulder bags to wear and store items in!