I am the unfortunately the undisputed king of kidney stones. I had one about 15 years ago that got hung and I got an infection had to have surgery (how does "they have to go get it up an existing orifice" sound to you?). Feels like someones jumping up and down on your privates, don't it?
10 years later I find out they have come back with a vengance, several in both kidneys. They will only work on one side at a time. I had 8 surgeries in 2006 and several more in 07 to get ride of the stones and residual peices (I have a pill bottle full of leftovers at home - it's very disconcerting to feel one come out...). Believe me, if you can pass it naturally it's MUCH better than surgery/catheter/stint I PROMISE.
We found out I had a hyperparathyroid which was putting excess calcium into my system; had to have surgery to remove that in addition to the kidney stone surgeries. I am now on meds to try and prevent them from forming again; it usually takes a couple of years to form one.
Usually, if you can get them to your bladder, they will pass (unless they get stuck at the exit point, which can be excruiating). There is some meds for that to help keep the pain down so you can pass them.
Best thing you can do is hydrate. Drink so you have to pee all the time will help flush it out.
Lastly, once you get one, it's a signal that you will always be susceptiable to getting them again. They show up on an x-ray i hope you only have one.