Nail trimming can seem scary, but it is very important that your puppy get used to having their nails trimmed. Keeping your puppy's nails short helps give them traction and walk normally. Nail trimmers come in two styles, guillotine and scissor. I have found that it is easier to see what you are trimming with the scissor style, and they have lasted longer. When clipping a dog's nails, it is important to avoid the blood vessel in the nails, or the "quick." Cutting too far can result in bleeding, but it is nothing too serious. Using dipstick powder or kwik-stop as a clotting agent will stop the bleeding quickly and help the toe heal. Of course, if the toe continues to bleed without stopping even after a clotting agent is applied, it is important to seek immediate veterinary care. If the thought of possibly making your dog bleed is too much for you, you may want to invest in a wireless dremel nail grinder. I prefer using these, as it helps you get the nails a lot shorter and smoother without causing any bleeding. With either of these options, it is always important to desensitize a new puppy to having their feet messed with and nails trimmed. I will link an article about trimming your dogs nails at home.
An inclusive checklist for bringing home a new puppy (straight from the mouth of a dog bather, vet tech student, and dog lover all in one). I linked many informational articles as to why you need these things, and what considerations you should make when choosing your new puppy supplies.