What's wrong with just walking up to someone to talk about the weather? ... worries about an upcoming test? ...a teacher who's a bit of an asshole?
Sheesh... since when has meeting someone had to be rigorously planned out? It's spontaneous... you just start talking... note their reaction and input... and go from there... You have more to lose by not trying... than you do if you trip over your own tongue. At least in the latter scenario... you had a chance to talk with her.. whereas remaining silent won't afford you even that much.
You're a smart guy... improvise...
"The weakest soul, knowing its own weakness, and believing this truth that strength can only be developed by effort and practice, will, thus believing, at once begin to exert itself, and, adding effort to effort, patience to patience, and strength to strength, will never cease to develop, and will at last grow divinely strong."
- James Allen