With things that are potentially sharp or jagged you do not normally want to induce vomiting as it can usually do more damage coming back up than passing through the intestines. The normal recommendation for something like this is to feed a bunch of very bulky stuff - like bread- very soon after ingestion so that it can cushion the sharp material as it passes through. This should be passed within a day or two if there are no complications. If you are noticing vomiting or diarrhea that continues for more than a couple of days or if the dog becomes listless or painful you will need to bring them in to the vet. Most of the time dogs can pass things - but occassionally they can cause real problems and may even cause blockages or require surgery. If you are noticing anything out of the ordinary - beyond mild digestive upset - I would not waste anytime getting into the vet.
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I have heard of the cotton balls as well - but feel that bread is safer.
I would also feed a bland and bulky diet of boiled chicken and rice (2/3 rice) for the next few days. The blandness will help with any digestive upset and the bulkiness will help to regulate peristalsis and keep the intestinal contents moving.
I hope all goes well.