Trimming nails is not as difficult as people imagine. If you make a mistake, it's not the end of the world. I have never seen a dog or cat hemorrhage to death from a mis-cut nail. In fact, trimming nails too short seems to be more traumatic for the trimmer than the trim-ee. A few general points before starting:

• Try to get your pets used to having their feet handled when they are young. For puppies, have them sit quietly in your lap as you play with their toes, examine their nails, feel between the pads, left the feet, turn the foot over, and generally get intimate with every bit of foot anatomy. They will soon find this procedure boring and allow you to do it without getting stressed.
  
  
• Get your kitten used to lying quietly on his back on your lap while you play with feet, extend the claws and press on the pads. As with puppies, this is best done when the kitten is sleepy, rather than when he wants to play "attack the hand that feeds me".
  
  
• Whether you are starting a puppy or kitten on the road to being a well-behaved trimming victim, start slowly. Do one foot at a time, maybe. A few toes. Both front feet. Whatever you feel comfortable with.
  
  
• Make a quiet sneak-attack.
  
  
• Try not to make it a big production of noise and over-restraint.
  
  
• Be mentally prepared to make a mistake, and know what you are going to do in the event that you "hit the quick" (see below, and see the page).
  
  
• Invest in some kind of styptic or coagulant powder to use when you hit the quick, and have it open and ready whenever you trim nails. This stuff comes in many brands, usually with descriptively gory names like "Clotisol" and "Kwik Stop". You may be able to find silver nitrate sticks, though these tend to cause a lot more stinging than the powders. More about how and when to use these products on the Nail Trimming Disasters page.
  
  
• Do not make a big deal out of the event if you do nick the quick. The dog or puppy will likely wince or yelp, but the discomfort will be short-lived and he will forget about it in a few seconds. If you make a huge deal of it and fuss over him like you've just amputated his leg, he will believe it is a big deal and start to react and carry on. Not what you want! Instead of, "Oh my heavens, I'm SO SORRY Marvin, what a poor puppy, you POOR THING! Mommy is SO BAD! Do you need a transfusion?" you want to convey, "Whoops, sorry pup, life happens, let me get some powder on that ..." and continue on like nothing of import occurred.
• If your puppy struggles for no reason (you haven't just hurt him), try not to let go and give up. Most puppies will test your resolve. If they can squirm and whine and make you let go, they have won. You are rewarding the naught behavior (whining, pulling away) by letting go of the dog and giving him his way. He will remember this for a looooong time, and put up a fuss every time thereafter. Don't let this start! If you can hang on for 10-20 seconds (the average tantrum duration) until he calms down, you will have won. At that point I usually make the symbolic gesture of at least trying to trim another nail before putting the foot down and praising the puppy grandly for such good behavior.
  
  
• Giving food rewards while trimming nails may be counter-productive. It does distract the dog, but also makes them more excited and squirmy, increasing the risk of an accident.