How do I execute well-timed taunt kills?

My best advice is to predict where the enemy is going to go. For example, if an enemy was going down the vents in Turbine, you may want wait behind a bend and initiate your taunt kill, so that it will hit the enemy when he turns the corner.

One particular taunt kill I got, I saw a Soldier coming up the path. I retreated and waited behind where he was going to pop out of, and taunted.

If your goal is specifically to get a taunt kill, you may want to favor certain classes. Heavy has the fastest taunt kill, with Pyro's Hadouken slightly slower than the Heavy's.

If you like to use the scout, and you have the sandman and the bonk energy drink, you can always drink your bonk and then taunt with your sandman to be sure you won't get killed.

Pick your target well.

The worst classes to target are Scouts, Pyros and Medics. These are classes that are constantly moving around and trying to be unpredictable. You are not likely to get a taunt kill on any of them unless you are really lucky.

The Spy is also not a good target. You won't often know where he is anyway, and if you botch, he can destroy you with a single backstab very quickly.

Soldiers and Demomen move more slowly on the ground, so you can try to catch them unaware, but do NOT try to taunt kill them if they are rocket jumping, sticky jumping, or demoknighting.

That leaves you with Heavies, Engineers and Snipers, your best taunt kill targets.

Heavies move very slowly, and are easily distracted by their own machine gun. Unless you have perfect timing it is NOT recommended to ambush them around a corner, as they will likely tear you apart with their machine gun before you can get your taunt off. Flank them from behind when the rest of his team is distracted, then strike.

Engineers tend to feel pretty safe around their nests, which means they stay in one place a lot and go back and forth between specific points on the map repeatedly. Be careful though of their sentry.

Snipers.

Snipers are the absolute easiest class to taunt kill.

They will focus down their scope for days, completely oblivious to the world around them, feeling perfectly safe wearing their razorbacks. Even huntsmen snipers tend to focus just before a shot.

So there you have it. Heavies, Snipers, and unaware engineers are your best targets. Soldiers and Demomen can sometimes work too, but you'll have a very hard time getting Scouts, Medics or Pyros taunt-killed, and Spies can be too dangerous.