How do I give first aid to someone who is bleeding?

External bleeding you can see while internal bleeding you can't see. Both will require first aid/medical attention. The seriousness of an external wound doesn't always correspond with the size of the wound or the amount of blood lost. For example, a small superficial scalp wound may bleed heavily because of the rich blood supply to the head. Bleeding from an artery is more serious and will take longer to stop. You may only see signs on the outside of the body, such as bruising and swelling, indicating a bleeding injury inside the body. Wear gloves or a barrier of some kind when giving first aid.
  
                             The Do Nots First:
Do not apply a tourniquet unless trained to do so.
Do not push anything back into the skin.
Do not apply antibiotic cream unless wound is minor and cleaned first.
Do not remove blood-soaked bandage.
Do not put pressure on an object sticking out of a wound.
Do not use pressure points nor elevation
 

                                       WHAT TO DO:
FIRST AID FOR SEVERE BLEEDING:
Call for medical help.
Apply continuous firm, direct pressure to wound, using clean cloth or bandage until bleeding stops.
If bleeding soaks through bandage:
Do not remove the original bandage.
        Apply more bandages and pressure.
Get medical help to cleanse and close the wound.
Monitor and treat for Shock if present.

FIRST AID FOR MINOR BLEEDING:
Clean the wound with soap and clean running tap water.
Apply continuous firm, direct pressure to wound until bleeding stops.
Once the bleeding stops, apply antibiotic ointment.
Cover with dressing.
If bleeding soaks through bandage:
              Do not remove the original bandage.
              Apply more bandages and pressure.

Giving first aid depends on what the person's major problems are. If they are not breathing, then CPR or chest compressions would be more important than the bleeding. If they are breathing fine and do not have any other major injuries, or the bleeding is the major injury, then direct pressure should be applied directly to the wound. This pressure will help the wound stop bleeding or at least slow down.