Once at 100°C it would stay there while the water boiled away.

How much energy? It depends on the substance, of course!
To melt a substance, you must add the "heat of fusion" and to boil it, you must add the "heat of vaporization". This is typically given as "L". For water, Lfusion=3.34E5J/Kg and Lvap=22.6E5J/Kg
To find this amount of energy, use this equation: Q=mL
AN OLD PROBLEM MIGHT LOOK LIKE THIS:
How much heat does it take to get 2Kg of water from 90°C to 110°C?
Your answer would have been Q=mcDT=(2Kg)(4190J/Kg°C)(110-90°C)=167600J
However, now we see that we are wrong, because the temps given overlap the phase change for water at 100°C. We must heat the water to 100°C, then boil it, and continue to heat it to 110°C.
Let's break the problem into steps...