Hermione is a witch, who while she should only be in her sixth year of schooling is still way advanced. Ask her just about anything magical in the HP-verse and she's probably read about it. I'm so not listing off all the spells she can do, but HP canon seems to have a spell for just about everything (within reason). Also, she kinda rocks the potions and seems to have a real thing for Polyjuice Potion to make someone look like someone else, thank you new canon. She also needs her wand to do anything at the moment.