I am assuming this is a tumbled stone, not cut as a jewelry stone with a flat back and definite shape. If so, let me know and we will go one more time.
Here is the answer for a tumbled freeform stone.
The kind of jewelry part (called "finds" in the trade) you want is a bell cap. There are different styles of this. You should be able to find these at crafts stores and if you want gold or perhaps sterling, a jeweler should be able to order for you. A few crafts stores will have sterling findings but most will have only plated items.
To attach the stone to a bell cap, a good adhesive should be used. There are two primary types of adhesive for this purpose. The first is 2 part epoxy cement and the second is a thick single part craft glue. There is a difference in the two: Epoxy takes more set-up time, meaning the cap must be set-up in place on the stone while the epoxy cures. The cement has no strength until some time has passed after the two parts are mixed. The epoxy has the advantage of curing with an almost unseen line and is a neater application.
The thick craft cement will hold the cap in place even when uncured and all may be set aside for a day while the cement cures. The disadvantage of this glue is the thickness and it will show a bit. Still, many crafters like the thick glue because it holds quite well in many kinds of cementing jobs.
Take the bell cap and press onto the part of the stone where you want it fitted. Try to fold the "arms" of the cap to match the contour of the stone fairly closely. Then when cement is applied, all is already fitted to the shape of the stone.
With either cement, do what many folks skip and help insure a good lasting bond. Simply clean the metal cap and the stone with alcohol (household medicine cabinet variety is fine) to remove any traces of oils from the surfaces. Allow to dry and then apply the cement.
Brands recommended: Should be available at crafts stores.
If not, a good craft store should have suitable alternative brands. I do not recommend the 5min cure types since working time is very short. You are better off to support the stone with the cap fitted and set besides for a couple of hours and get a stronger bond. Keep the leftover epoxy mix on the same scrap baggie or whatever you mixed it on, along with the toothpick (or whatever mixing tool). When the leftover cement is cured and the tool is stuck to it firmly, you know the cement is cured. This tells you your jewelry item is ready without having to mess with it while the cement cures.
E6000 crafts cement. This is the one part thick glue. Apply sparingly since it will squeeze out a bit and will settle down to a smoother surface. Be careful of "stringers" of cement on the application tool (again, toothpick or what is handy) since these stringers are messy getting on the wrong places. When cured, the cement may be peeled off of places it should not be.
You will need a "jump ring" (wire loop) or "snap on bail" to hang the stone from a chain. These are also available at crafts stores or at a jewelry store (generally not in mall chain stores, try local folks).
Just do a dry run first and then cement away! Use as little cement as appears needed for a neat and less "crafty" looking finished job.