When a patient is bleeding heavily from a wound, the immediate priority is to control the bleeding. The best initial action is to apply direct pressure to the wound using a clean cloth or bandage. This helps to stem the flow of blood and allows time for clotting to begin. Elevating the limb can also help reduce blood flow to the area, but applying direct pressure is the primary and most effective method. Tourniquets are used only as a last resort when direct pressure and elevation do not control the bleeding.
Reference:
American Red Cross First Aid Manual
Emergency Care and Transportation of the Sick and Injured (AAOS)