Don't go into it with the mindset that you want to ask her out... You see if you get so fixed on asking her out then your blinded when the perfect oppurtunity arrises to actually ask her...
Your gonna want to try to establish eye contact, which is a hell of a lot easier said then done. Try to establish it in a way that your checking to see if shes interested("Omg he's totally looking at me!11!!!!11!1! Gabby how does my butt look?) but your not just staring at her("Try it motherfucker I got a loaded .44 waiting for you
")If she establishes eye contact with you(and doesn't start mean mugging) or you know she knows your interested but shes to shy to look you in the eyes, then what you do is lift your ass out of your seat, put one foot in front of the other, walk over to her and say: "You know we've been in this class for what 3 months now? We never really got the chance to talk, it'd be a shame if we didn't don't you think?"
Uhhh son that line was dope, alpha to the bone... if delivered correctly. Remember confident yet sensitive...