Please see http://vetmed.iastate.edu/HumaneEuthanasia for updated materials!

Once the animal has been rendered unconscious, exsanguination procedures should be initiated to ensure death using a pointed, very sharp knife with a rigid blade at least 6 inches in length. As indicated previously, exsanguination procedures are required with the use of penetrating captive bolt. The knife should be fully inserted through the skin just behind the point of the jaw and below the neck bones. From this position the knife is drawn forward severing the jugular vein, carotid artery, and windpipe. Properly performed, blood should flow freely with death occurring within a few minutes (See diagram at right).

Alternatively, one may sever the brachial vasculature by lifting a front leg and inserting the knife deeply into the axillary area at the point of the elbow and cutting the skin, blood vessels, and surrounding tissue until the limb can be laid back away from the thorax of the animal. Regardless of the method used, great care should be exercised in performing exsanguination procedures. Although unconscious, animals in this state are capable of violent involuntary movement that may cause personal injury (See diagram below).
Exsanguination by severance of major blood vessels in the neck:
1) Jugular Vein, (indicated in blue color),  2) Carotid Artery, (indicated in red color), and  3) Trachea or Windpipe (white tube).