Vomiting blood could be caused by many things including a non-food item in your dog's system, which may have punctured your dog's stomach, Poisoning, ulcers, a blood disorder, and more. It could also be that your dog cut it's mouth and swallowed blood and is now vomiting it up. If an ulcer is to blame, you can give your dog some pepcid or Zantac. Read about Pepcid dosages and usage information here: http://www.petplace.com/drug-library/famotidine-pepcid/page1.aspx
Zantac can be given to a dog at .25 to 1mg per pound every 8-12 hours. Read about usage here: http://www.petplace.com/drug-library/ranitidine-hcl-zantac/page1.aspx
Check your dog's mouth to see if he has a wound in his mouth or a tooth that's bleeding. If it is not swallowed blood, I urge you to get your dog to the vet.
You can read more about blood in vomit here:http://www.petplace.com/dogs/hematemesis-vomiting-blood-in-dogs/page1.aspx
I hope you find this information helpful.
If she swallowed an item that could have punctured her stomach leading to bleading, then it we would not advise inducing vomiting since it could cause more damage coming up then passing through her system. When a sharp item has been swallowed, we recommend feeding a piece of bread or rice to help cushion the sharp edges as it passes through. You will need to keep an eye on your dog's stools to see if what ever was swollowed passes through your dogs system as well as for signs of fresh blood or mucus.
Fresh blood or mucus indicates inflammation within the large intestine while dark black or tarry looking stools indicate bleeding in the stomach or small intestines. If your dog's stools become black then your dog should see a Vet immediately. If your dog begins to vomit, has a lot of diarrhea, becomes unresponsive to you or squats without having a bowel movement then you should take her to the vet immediately as well
You can read about the effects of an intestinal puncture here:
If it was a non sharp item, the vomiting could be induced using instructions found here:
But with there being blood in vomit, I would not recommend inducing vomiting.