Number 3 explains how guns and suicides are linked. I've also posted medical studies and government studies from the Journal of the American Medical Association, the CDC, UPenn and the Australian Institute of Crime which were ignored and thus I can't be fucked to bring back up.
But the cracked article does the best job in my opinion of explaining it, because it also mentions other notable examples of banning (or fool-proofing) popular suicide methods causes a decrease in suicides attempted. People can say "Oh, I'd just go down to the train tracks" or "I'd just slit my wrists" but once you get past the conjecture, that isn't the case for most people. Most people attempting suicide want a quick and painless death, and guns are quick to use (just pull a trigger) and can easily cause instantaneous death if pointed at the head and brain.
Thus, banning them would lead to a decrease in suicides attempted (as would instituting longer waiting periods, removing the "gun-show" loop-hole, and requiring mental health checks to buy guns).
