Typically, sudden extreme debilitating pain is very effective in making people keel over without a sound, as the surprise stops them from crying out initially and the follow on pain causes them to lose consciousness.
Surprisingly, certain stealth kills in Assassin's Creed are actually accurate in this, as inserting a sharp piece of steel ~6 inches deep would be very effective, particularly into the brain (via the eye or the base of the skull where the spine connects) or the heart via the ribs.
Puncturing a lung would also be effective as often the goal of a stealth 'kill' is to incapacitate someone quietly rather than kill them.
I agree that stealth kills as generally depicted in media are either completely over the top (Tenchu series) or borderline ineffective as the victim would have a chance to retaliate.
A standing rear naked choke is usually quite effective combined with walking backwards which both pulls them off balance and adds their body weight to the choke.
As the article points out, when performed correctly, loss of conscious is very rapid (personal experience confirms this) so the target generally won't have time to draw a knife or otherwise sound an alarm.
About the only armour that would protect against this would be some form of rigid neck protection (padding wouldn't help), which I don't think is too common these days outside of bomb suits.
Depends on the training. I vaguely remember this coming up in an earlier version of this thread and reiterating what a Royal Marine told me, you use the tip of the knife into the side of the neck, ripping out the front through all the structures in the neck (muscles, blood vessels, windpipe potentially).
Typically, you grab hold of their mouth and restrain them while they die.