Secondly, whether or not you have an adequate supply of platelets in your blood. These are microscopic fibers that are attracted to areas of bleeding. They form a "clot" on the bleed and cause the bleeding to stop.
If both of these coagulation systems are normal and, depending on how large the "vein" is that is bleeding, you should stop bleeding fairly quickly (inside of ten to twenty minutes) if you do nothing but let the wound bleed. If you are not suicidal though and have any common sense at all, you would simply apply pressure to the bleeding area and the bleeding would stop even quicker as long as you hold pressure there.
If there is an artery involved, the bleeding could last much longer. The reason is that there is significantly more pressure on an arterial bleed than on a veinous bleed. This keeps the platelets from doing their job. It would be like trying to stop a garden hose with a fireman's nozzle on it. The pressure would not allow you to stop it quickly so you'd have to stop the flow at the source. Again, you'd want to hold significant pressure and get to the nearest ER so they could stop the bleeding for you.
Luckily, the veins are closest to the surface so you're most likely to hit a vein rather than an artery but arteries are knicked fairly often.