The part of the toenail with a deep, distinct groove is the dead area. There is no nerve or blood vein in that section and you may safely cut it off without harming the dog. Worrying about where and how much to cut makes many people nervous and this nervousness is easily felt by the dog, making him jittery and more inclined to struggle. Until you feel confident in your work, cut just the very tips of the nails. As you become more skillful and your dog more cooperative, you'll be better able to estimate the amount you can safely cut and decrease the sessions to twice-monthly.
Accidents happen once in a while and even the best groomers occasionally draw blood.
Nails can bleed heavily and it's wise to have something on hand to stop it. A pinch of flour applied to the end of the nail will work but more effective is a product like Kwik Stop that is designed especially for that purpose. You can find it at your local pet supply store and a tiny container will last a long time. It does sting a little when applied to the nail but stops bleeding almost immediately. Since some dogs will be reluctant to allow you to cut another nail near the wounded one, I usually leave that foot for a moment and work on another, going back to the first when I'm through.