Guys, this is a pretty simple and ordinary situation you've probably come accross before..

I'm in my second and last year of 6th form, theres this popular chick in my psychology class (6th form/colledge) and theres only 4 students in this class.

She doesnt sit near me and i cant move cos its set seats now so it'd be wierd..
I'm not hugely popular, would like to be, but im not unpopular either, i get on with a bunch of the populars, and even a few of this HB's friends..

Basically she's been looking at me and smiling a lot and im taking that as IOI, but like we've never actually talked (She does know who i am though), and I want to know how you think I should approach this girl, and build attraction without it being so fucking obvious in this situation, as theres only like 100 students in the whole of sixth form, so everyone would notice pretty easily..

So i need it to be natural and not obvious.. how do i approach her and start a conversation with her?

I'm thinking it could initially be something to do with the psychology and then lead into general convo.. if so how do i lead into general convo.. if not this way then how do i start a convo with her?

Say Hi. Literally, best piece of advice I can give you. Universal opener. It's simple.

Scenario:
You: Hi
Her: Hi
You: (you trip over your words, you stutter, whatever)

You learn from your mistakes and do it better for the next girl.

Honestly, I thing your chances are slim with this one.
Why?
Because you hesitated in the beginning. You must approach and at least introduce yourself in the first opportune moment.
But still you can benefit by learning on this girl a lot. Since you will probably not get her, you can experiment, try things without a fear that you will screw up..

I would actually try something like this.
You: Hi. *smile*
Her: hi..
You: Pretty boring lesson today, eh? *excited* Ohh, By the way!! Did you see the fight outside school in the morning?! OMG It was hillarious! (go to the Style's Routine - "Two girls fighting outside of a Bar" or whatever it is called)

This should get her attention. Then move on to any topic you like, teachers, kids, relationships whatever.. You are learning so it doens't really matter..

_________________
Life is either a daring adventure or nothing.

My .02 of advice would be just say hi and comment on something in the class. Test you just had, one coming up, project, that day's class etc. That way you're coming across pretty casual like you said you wanted. Then from there after you've said a few things about the class or whatever you can keep going or do whatever you like from there.