Can you suggest any painless way of clipping my dog's nails?

Yes.  This is why God invented Vet Techs - although the last time the Vet Tech clipped MY dog's nails she cut too short and my dog was injured, an injury that later infected.

It's the same as cutting your nails?  Does it hurt you when you clip your nails?

don't buy a cheap clipper. it should be a sharp, high quality one.

don't clip the nails close to the blood vessels. 

I've seen lots of idiots clip close to the blood vessels, and it's no wonder why the dog is in pain.

Nail clippings shouldn't hurt, although if your dog is crying while having it done, I'd say go to a Vet instead of where you're at now. My dog hates his nails clipped and will only let the vet do it, I don't know maybe he likes him? anyway go to a vet.

Remove the paws

What I have been using is one of those battery powered excess skin/calluses on feet.  It works great on toenails.  Theirs & mine too.  It doesn't make as much noise as some the the things I've tried.

Take the dog to your vet.  They can do it safely and w/o pain of clipping too short.

Nail clipping is painless as long as you dont go past the quick.

There are no painless ways but it shouldn't cause pain if you do it correctly. Why not take him/her to a vet?

If dogs are walked daily on pathways /hard ground then they naturally wear their own nails down, so reality is if you are exercising your dog correctly there should be no need to clip its nails at all.

If a dog needs its nails clipping, then little and often is the key, not only for them to get used to nail clipping and touching their feet ....easier to clip are white nails, black nails more difficult to see the quick and the longer you leave it the longer they grow and the quick grows down the nail which means it is easy to cut into the quick and it will bleed.

My advice is don't buy guillotine type, buy the scissor type, you can buy nail grinders and a sanding block can also be used if your dog is unused to or fearful of the noise from the grinders. Many dogs are not used to having their foot held and that causes many to 'fight' nail clipping along with an owner who is unsure of what they are doing, so you need to be confident when clipping nails

Don't clip them so short.  If you are incapable, have a vet show you how to do it properly.  Just take off a little at a time.