You really need a razor sharp knife. Razors are pretty tricky to hold when they are covered with blood.
Certainty: possible if you cut an artery, improbable otherwise
Notes: Painful at first. Danger of discovery. This is a very common suicide 'gesture' and hardly ever results in anything other than a scar. A lot of will power required to cut deeply into groin or carotid arteries, which are the only ones likely to kill you. Don't bother with this method. Cutting your throat is difficult due to the fact that the carotid arteries are protected by your windpipe (feel where your arteries are with your fingertips, & slice from the side). I've seen photos of people who have used this method - the depth of the cut required is amazing. If you want to cut your wrists, cut along the blue line (vein) on the underside of your wrist, but cut deeply so that the artery underneath is exposed. Cut this lengthways with a razor or similar. The traditional hot bath does help, since it keeps the blood flowing quickly, slows down clotting, and is nice to lie back and relax in. Position yourself so that your wrists don't fall inwards against your body, blocking off blood flow. Now all you gotta do is watch the water turn red b4 you pass out :)