What you do will depend on whether the stone has any hole drilled in it or not. If it has a hole front to back, you need a finding called a "bail" then you can string it onto any kind of chain or necklace you choose. If there is a side to side hole, then the necklace can be strung through the stone if it is fine enough, if not you can put wire through the hole and make some loops to attach to a necklace or use a wire choker type necklace. If there is no hole, then you need some kind of mount. If it is a flat backed stone, you can put it into a bezel. If it is an irregular shaped stone, finding a bezel just the right size will be impossible. A DIY metal bezel will require you to do some soldering. But there are other creative ways of doing a bezel. There are beaded, crocheted, wire wrapped, and macrame bezels. Googling any of these will bring up tutorials.
But if you're talking about a faceted stone, with a pointed back, a jeweler's pronged setting may be the way to go.
Hope this helps. If you have any more questions, I'll try to answer.