When dealing with bleeding wound:

Priority #1 is to stop the bleeding. 

Below are several rules to keep in mind:

• Maintain composure, no need to panic
• In most cases, bleeding can be stopped by applying pressure to the wound
• Bleeding generally looks much worse, than it really is.
• If the bleeding is not stopping, apply clean cloth or bandage to the wound for 15 to 30 minutes with reasonable amount of pressure. 
• Make sure the cloth stays in place and is not moved during that time, as movement can re-aggravate the wound and cause bleeding to resume. 
• If the bleeding persists, apply the second dressing to the wound and increase the pressure. 
• As mentioned above, you can control or stop the bleeding in majority of the cases with pressure alone.

Priority #2 is to keep the wound clean. 

This will minimize the chance of the victim getting an infection.  If water source and soap is available, wash the wound.  If not, and there is visible debris, extract it with your hands or tweezers. Contact emergency services if the bleeding has not stopped or you suspect potential for infection or internal injuries (fractures, brakes, head injury, etc.).  For small wounds and scrapes, it is generally advised to use triple antibiotic ointment, which is the best in preventing infections. 

Here is a quick outline of first aid steps:

• Involve the victim, if able, to apply pressure on the wound while you are putting on protective equipment or taking care of other wounds
• Stop the bleeding by applying pressure to the wound with dressing
• If not effective, apply second dressing and attempt to increase the pressure on the wound
• Contact emergency services, unless the wound is minor or you are confident that there is no need for further intervention