I always clip my dog's claws in good bright daylight, or bright artificial light, and with the light kind of shining through the claw, so that I can clearly see the 'quick' (the very sensitive pink area inside the claw) Also I never cut too closely to this, just trim the claws little and often. And if your eyesight is not too good with up-close small detail, put on some reading glasses to be sure.
There is nothing more likely to traumatise your dog, and make it clipper-shy for the rest of its life, than accidentally cutting to the quick!
Your best bet is to talk to your vet about sedation, particularly if your dogs take any other medication. I seem to recall there is an over-the-counter medication for just this problem, but my memory fails me as to its name. :-\
I'm pretty certain our co-CL, Ghilly, knows what it is, so if she doesn't check in on this thread, send her a private message and ask her to weigh in here. You can also check with our veterinarians here at Med Help on the Ask a Vet forum for advice on sedation.
In the meantime, make it a point to start working with your dog's feet. It may take several months to get them comfortable having their feet handled, but it's well worth the effort. If they like to watch TV with you and have a petting session, start by rubbing down a leg and over the foot. Gradually work your way up to the point they will stay relaxed and allow you to examine all their food pads and in between the toes. Some dogs are more frightened of the sound of the clippers and react badly as soon as they see them. Once your dog is comfortable having his feet handled, do the foot-handling exercise with the clippers next to you where the dog can see them. Next step - merely place the clippers on the claws one at a time, but don't cut. Once they're totally comfortable in the presence of the clippers, try clipping and allow the dog to calm down in between cuts.
If you start this exercise with a puppy, this problem will never come up. It just takes a little longer with older dogs who have already decided that clipping is a traumatic experience.