This article is from the rec.pets.dogs: Health Care Issues FAQ, posted to rec.pets.dogs newsgroup. Maintained by Cindy Tittle Moore with numerous contributions by others.
Most dogs need to have nails trimmed at some point. While the vet will often clip them for you, many dogs need their nails trimmed more often than that to prevent injuries and other problems associated with overgrown nails.
A tip: Look for illustrations of dog nails. Most dog care books will have one. Cardinal (a dog products vendor) provides a small poster that illustrates not only normal nail clipping but also how to gradually work back the length of nails that have grown too long and is quite informative.
Clipping
Use nail clippers available at pet stores. Look for the guillotine type (don't use the human variety, this will crush and injure your dog's nail) and get blade replacements as the sharper the blade is the easier this procedure is. There is another kind that looks like scissors with hooked tips that are also good, and may be easier to handle (however, the blades cannot be replaced on this type).
Before cutting the nails, examine them carefully. If the nails are are white, the difference between the nail and the pink quick is easy to see (use good lighting). If the nails are dark, it will be much harder to tell where the quick is, in which case you must take care.
If your dog resists having its nails trimmed, try trimming them while you sit on a couch with the dog on its back in your lap. By putting the dog on its back, you make the nails accessible and put the dog in a submissive position where they are less apt to fight. As with many things, this is easiest if you start while your dog is still a pup.
If the cutter is sharp, the nails won't crack if you cut at right angles to the nail. that is, hold it so that the blades are on the top and bottom of the nail, not to the sides of the nail.
Do not cut below the quick. It will be painful to your dog and bleed everywhere. When in doubt, trim less of the nail. It will just mean trimming more often. Clip the portion above the quick for each nail and don't forget the dewclaws. Keep a styptic pencil on hand to staunch any blood flow. Flour or cornstarch will help in a pinch.
Dewclaws are a "fifth" toe, positioned as a "thumb" to the rest of the nails and they do not touch the ground. Not all dogs have them, and they may be found on the front legs only or on all four legs. Many dogs have their dewclaws removed when they are puppies to prevent infection resulting from easily injured dewclaws. Some adult dogs that regularly tear their dewclaws should have them removed. While they take longer to heal than three-day old puppies that have had theirs removed do, the pain of periodically tearing them and going in to the vet to have them bandaged back up makes the surgery worth while.
Grinding
The nail grinder avoids the potential problems of cutting the quick, nails cracking, and sharp edges afterwards. The nails can also be thinned, allowing the quick to recede, resulting in shorter nails and a tighter paw.
RC Steele and other mail-order companies sell them for about $45. One model is the Oster Pet Nail Groomer, Model 129, with two speeds. Some dogs may be spooked by the noise. It may help to watch someone who knows how to use it first.
Filing
You can use a wood rasp and file your dog's nails down. Also, if you clip them, using a plain file afterwards helps smooth the edges down and keep them neat. You can use "people files" or purchase files shaped for this purpose.
 
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