Since I'm new to enchanting, and struggled with this...

When you learn Enchanting as a skill, you also, by default, learn disenchanting.  It's in your spellbook.  Look there and drag it to an action bar. 

I kept trying to level enchanting hoping the trainer would teach it to me, but I already knew it. (me == idiot).  Serching the forums was semi-frustrating to find out how bad I suck.