Take a close look at each of your puppy's nails. Some may be dark and some may be light or clear in color. Light and clear nails will show the quick inside the nail easily. Darker nails hide the quick, making it a bit more difficult to see. Clipping the nail without knowing exactly where the quick is can be worrisome.
If you take a closer look at the underside of your puppy's nails you may be able to see the quick easier or you will notice a split in the nail on the bottom. When cutting, do not go beyond this split, especially on the dark nails, because you may risk cutting the quick.
Choose the style nail clippers you will use for your young pup. You can use a guillotine type clipper or you can use a scissor type clipper. Both are easy to use, your choice is personal preference.
Once the nail is inside the clipper, apply a small amount of pressure. Avoid cutting the nail at this point. You want to gauge your puppy's reaction. If the amount of pressure you're applying is something your puppy feels, bring the clippers down closer to the tip and try again, having less of the nail in the clippers. If your dog does not react or flinch, he doesn't feel it and this is okay to cut.
Use your clippers to cut small amounts of the nail tip, slowly moving up the nail. Making small cuts on your puppy's nail gives him time to get used to this grooming procedure as well as gets you used to how short you can cut your little guys' nails while avoiding the quick.
Repeat this process for each one of your dog's nails. Don't forget his dew claws if he still has those intact. You may need to go a bit slower with even smaller cuts on darker nails until you are used to where the quick is and how easy it is to accidentally cut.
Accidents happen, especially if this is a new procedure for you and your puppy. If you happen to accidentally cut the quick you can apply styptic powder or baking soda to stop the bleeding. A little extra tender loving care and a treat may also help your dog deal with the pain and tenderness. Next time, go slower and be more careful, but know your little guy will forgive you if this happens.