Bleeding
Minor bleeding can be stopped by applying pressure to the wounded area. Apply pressure until bleeding stops, and then dress the wound.
Arterial wounds require additional effort to stop the bleeding. If blood is gushing out of a wound, it's going to take more than a little pressure to stop the bleeding. Try applying direct pressure to the bleeding end of the damaged vein or artery.
If the wound is to an arm or leg, a tourniquet can be applied to the injured limb. It needs to be placed on the limb between the wound and the victim's heart. Never apply a tourniquet to someone's neck.
My personal preference is a Combat Application Tourniquet, which is a specialized device I keep in my bag. It's not too expensive and is easy to use. With a bit of practice, you can learn to apply one to yourself in less than a minute and to someone else in 30 seconds or less.
In a pinch, a torn-up shirt or a length of string or rope will work almost as well. Tie the cloth around the limb above the wound and use a stick to twist it tight enough to stop the flow of blood. Good luck applying this type of tourniquet to yourself.
This is where having a doctor on hand can really help. Arterial cuts don't normally heal on their own and require special care. Leaving a tourniquet on for an extended period of time can lead to permanent damage to or loss of the affected limb. In order to avoid damage, release pressure once every 15 minutes for a couple minutes so blood will continue to flow to the rest of the limb.
Don't continue to do this if the wound starts gushing blood as soon as you release the tourniquet.
Always clean and disinfect the wound and the area around the wound to prevent infection.