I'm in the city of Stormwind in the Mage Quarter where I talked to the Master Fire Eater. The 2nd quest in his training is for you to light torches, throw them up in the air, and catch them four times in a row. However, I can't figure out how to do it. What I can figure out is that standing near the big bond fire is sufficient to light the torch, and to throw them I only need to click on the button that appears next to the objective on the right. However, after that I am at a loss what to do. How does the mechanics of the torch catching work? How do I know if I caught the torch? Is there a counter to tell you how many in a row you've caught?
You must juggle with the torch. When you throw it, try to follow it and to stand where you expect it to land. If you are close enough to the land point, you will "catch" it, and it will bounce instead. If you weren't close enough, it will burn you for some of your HPs. Movement abilities such as Sprint or Blink may help.
Make it bounce four times in a row, and you win.
Click the quest button while standing near the bonfire to throw the torch. You should see the torch move away in an arc, and the shadow of the torch on the ground. If you don't see this, try throwing from the other side of the fire. The torch always heads in the same direction when thrown from the bonfire (over to a "catching area").
To catch the torch, position yourself under where the torch will land. If successful, the torch will throw itself in another direction. If unsuccessful, the torch will detonate - you must start over.
This quest is available in many capital cities. If you're having trouble where you are, try a different city. I recommend Ironforge for Alliance and Silvermoon for Horde (flat catching area with little in the sky to block your camera).
"Strafing and mouseturn" in depth:
Hold right mouse button down on the screen to start mouse looking. You can drag the mouse left or right to turn your character. During torch catching, you should hold down the mouse button the whole time!
While doing this, you can strafe to get anywhere you need to go. For example, if the torch thrown forward and left relative to your facing, just move the mouse right to put the torch on your left while you are strafing left. You should be in motion the whole time!