There are a variety of nail trimming supplies which you can purchase at your local pet store. Nail clippers come in several varieties including the guillotine type or the scissors type. Use whichever style you feel most comfortable with; most people say that they find the guillotine trimmer most convenient. If you (or your dog) are extremely anxious about the nail trimming process, you can purchase a nail grinder.
It's easiest to trim light colored nails. When you trim the nail, make sure to cut above the quick or pink colored center of the nail. If you cut into the quick, your dog's nail will bleed. If you have a pet with dark colored nails, trim very small amounts of the nail to make sure you don't cut into the quick. If you do cut off too much of the nail and your dog starts to bleed, you can use flour or cornstarch to stop the bleeding. Don't forget to trim the dewclaw, a small claw attached to the leg just above your dog's paw.
If you have a puppy, it's important to get them used to a nail trimming routine. Start by regularly trimming small amounts of the nail every week and reward your puppy with treats after the trimming is done. After a while, your puppy will learn to not be anxious when having his nails trimmed because the routine will be familiar.
If you have an older dog who does not like having his nails trimmed, you may want to ask a friend or spouse to assist you when you trim his nails. One person can gently restrain the dog and the other person can do the nail trimming.
Remember---the key to making this chore an easy one is to make it a positive experience for your dog. Tackle this project when you are calm as your dog can sense your stress. Praising your dog and talking to him during the process can do wonders and will reassure him that nail trimming is not a horrific thing. After it's all over, remember to reward his good behavior with treats and more praise!