I have had several (caused by hyperparathyroidism, which is basically an overproduction of calcium in my body.) Two of them could not pass on their own, and needed lithotripsies in order to break them up. However, the lithotripsy machine at my hospital does not work well, and both times the stones broke up into smaller fragments which eventually blocked my kidney. I was admitted to the hospital each time in order to keep a continual IV going to get the smaller pieces through. Not a pleasant experience - usually lithotripsies go much more smoothly!
Regarding how long they will take to pass, it really varies on the size of the stone. If they are not big enough to break up via lithotripsy, just drink LOTS of water, and have your pain medication available. Each time I went to the ER they sent me home with Vicodin ES, but of course sometimes that did not work, and I needed to go in for a morphine drip and IV. With the amount of stones I had, they knew me by name in there!
Also, if possible, try and catch it when it finally does pass using a strainer. They will be able to test it and determine what type of stone it is, and sometimes give you more specific tips on how to avoid them. For example, since they determined mine were calcium stones, I got a long list of foods to avoid, and had surgery on my parathyroid eventually to get the calcium levels reduced.