Our upstairs toilet has developed a leak that is causing water to come through the ceiling. It only happens when the toilet is flushed. Where is the leak originating from?

Most likely a wax ring failure, any water dripping from the rubber gasket between the tank and toilet, or anywhere else? If no water is seen upstairs but leak is showing downstairs I'd venture to guess time to replace the ring. How to Replace a Toilet's Wax Ring | eHow.com (http://www.ehow.com/how_15276_replace-toilets-wax.html)

Bob is 100% correct. And great site also for changing wax ring. I would only add that you should flush toilet till tank is nearly empty, then plung any water you can out of the bowl, then use a spong to remove any water that is left in the tank and bowl. This way, you will have no chance of water spilling when you lay toilet over to clean bottom of toilet. Ive seen to many times when people don't take the time to spong out all the water and will make one heck of a water mess on the floor when moving toilet. It takes less than a minute to completely spong a toilet dry.(a shop vac works well for this too,)

Get another person to help you move that toilet and tank all at once and set the toilet on a piece of cardboard, or something similar.

At least is sounds like it's only the wax ring, which is a straight forward fix.

You have a ruptured wax seal that must be replaced.
Cyberheater said, "
set the toilet on a piece of cardboard, or something similar." and that's the correct way to place a toilet after it's been pulled.
Follow MGD77 advice about clearing out the tank and bowl but don't lay the toilet on its side. Leave it upright on a piece of cardboard. The reason being is that there's still a gallon of water hidden in the trap of the bowl that will come spilling out on the floor if it's laid over. About the only time I lay a toilet on its side is if I have to go in from the bottom to remove a object that's been dropped into it. Good luck, Tom