Just some basic tips for helping care for a toe nail that may be bleeding/torn/damaged. Always remember (especially with feet) that a dog may snap or bite if something hurts all of a sudden, so it would be safer to muzzle your dog.
Tip 1: Remove 'splinters' of nail if you see any. If these are left on they may cause more pain or even continue to damage the sensitive parts of the damaged nail. Sometimes the broken parts of nail can be simply pulled off quickly with your fingers, but clipping them at their base could help if you think that it might not be a good idea to pull it off.
Tip 2: Wash with luke warm water. You want to remove as much dirt and debris as you can to prevent infections.
Tip 3: The injury continues to bleed, apply a bit of pressure with a cloth. Grabbing the whole paw with your hand should work well if your dog will allow you to.
Tip 4: If large portions of the nail has come off, it will leave a senstive area (that would have been inside the nail), be careful the the dog (or you) do not touch it. Injuries like these should be looked at by a vet so that they can bandage and possibly give antibiotics to prevent infections.
Tip 5: If your dog's nail injury is caused by clipping too short, then you can stop the bleeding by putting styptic powder or corn starch.
http://vetmedicine.about.com/cs/dogdiseasest/a/torntoenail.htm