Ideally you should start when your dog is young to get the dog used to having his feet handled regularly. Desensitizing your dog to having his paws handled will have a few other benefits too: it will make it easier for groomers or your vet to handle your dogs feet and will also mean if your dog is injured you will be able to examine his paws easier.
If it's your first time clipping a dogs nails it might be a good idea to watch someone else do it first. Ask your vet or the groomer if you can watch while they clip your dogs nails.
You will need a special pair of clippers for the purpose. Human clippers of scissors could tear the nail and cause painful torn edges. Make sure you get the right size and type of clippers for your dog. You might find a nail file useful too.
You will also want to have some special clotting powder on hand just in case you accidentally cut the nails too short and it starts bleeding. You can find all these products at your local pet supply store.
You will want to clip the nails in a quiet place with minimal distractions. If your dog has never had his nails clipped or is particularly resistant you might want to ask someone to help you. You are after all poking at your dog with a sharp object and it could be dangerous !
To avoid mishaps its best to slowly desensitize your dog to having his paws handled. this part should be easy. Take your dogs paws and massage them a bit.
It makes the process easier if the dogs nails are softer. You can do this by bathing the dog beforehand, massaging some baby oil into the paws or even just dipping the paw into warm water. This has the dual effect of both softening the paws and cleaning the dirt out from under the nails.
Examine the nails closely and try to locate the cluster of veins. This is called the 'quick' and cutting this can cause your dog to bleed. If your dog has dark nails this can be difficult. The best policy here is to trim the nails bit by bit over a longer period of time. The quick will retreat over time.
Try to cut with the right hand and hold the paw firmly. Use a calm soothing voice while you do this. You don't want your dog to become afraid and make the clipping more difficult. Try to cut at 90 degree angles.
If you do cut too far - don't worry! You can use some of the powder to stop the bleeding. Just sprinkle the powder over the affected area or dip the paw into the powder. There are some other household items you can use to slow the bleeding. You can use cornflower or normal powder in the same way you use the styptic powder. You can also press the dogs nail into some soap. If the bleeding is not too bad - just simply applying pressure should slow the bleeding.
If you have cut your dogs nails too far and they bleed - this may make the dog scared of the nail clipping all over again. You will need to desensitize your dog again.
If your dog is very afraid of having his nails clipped you should gradually get the dog used to the process and the tools. Start again by praising and treating the dog while you handle his paws. Then get the dog used to the clippers. Step by step desensitization coupled with positive reinforcement should ease your problem.
If you really can't get your dog to behave long enough for a nail clipping remember - most vets will do it for you. Don't be afraid to ask for help.