I've been cutting my dogs' nails now for years. Done correctly, you will not draw blood nor will it hurt. Although, most dogs hate having their feet touched. It is always a good idea to have something on hand like previously suggested, just in case.
Also, if you soak your pets feet prior to cutting their nails, the water will make the nails less brittle and more pliable making them easier to trim. Trimming their nails after a bath is better than before for this reason.
Once while cutting our late Blacky's nails, he moved suddenly just as I was trimming and I cut pretty high up into the quik. He did bleed, but we managed to stop it with some styptic powder. Without it, it would have been much harder to stop. It is definitely a good idea to have it on hand in your dog grooming kit along with the trimmers.