Andrea, read it slowly:
In many cases it's impossible to ID corals down to the species level without dissecting them.
In short:
You would have to cut a piece of skeleton, soak it in various chemicals to kill and clean the animal (to expose the skeleton). They, you will need a dissection microscope - $1000 one or better. Oh, you'll also need a reference (books, articles) and be familiar with most scientific names for every little bit of the skeleton. Most corals can be identified (species) only by experts with a lot of experience and huge reference libraries.
Ready?