Mary, I used to work for a vet and have cut tons of nails -- guess what, every once in a while you get a bleeder!  I keep styptic powder (which is what Kwik Stop is) on hand, but all the suggestions -flour, cornstarch, etc work too.   When Dixie gets a bleeder, it's usually a lot because she is a big dog.  I use the styptic powder and actually have put paper towel with vet wrap on her paw just to keep the pressure on it and to keep from having blood everywhere.  Don't worry, they won't bleed to death!  Keeping them quiet will lower their blood pressure and slow the blood flow and help stop the bleeding   I've never had to bandage KS, because she is so much smaller and there never is as much blood.  Just try to cut the hook part of the nail (on clear nails it's easy to see how far back, so sort of judge the black nails by that).  Remember, the longer the nail grows, the longer the vein grows, so cut nails often.

Mary, I found this site which gives great directions and photos of how to trim.  Hope it will help you!

http://www.vetmed.wsu.edu/ClientED/dog_nails.aspx

Mary, another suggestion -- I use a cordless Dremmel grinder (about $20 at Lowe's or Home Depot) and "file" their nails.  This keeps the nail from having sharp edges, and if you do it about every couple of weeks and keep the nail short, you can actually encourage the vein, or quick, to recede.  You can do the same by keeping the nails trimmed, but you can just keep them shorter by taking a tiny bit off with the Dremmel.  And, I think it's easier to control getting bleeders.   If the nails have grown long, I clip the tips and then finish with the grinder.