How would you like to be approached?

Oh God, it's the apocalypse! A guy who may now know how to be normal and not clingy!

Ok, ignore that. I got a little hyper. Ok, we may meet, but i'll never know, so your looks don't matter.

Basically, the best approach, is have a life. Seriously, enjoy it with everything, with full force. A chick see's that, she'll be interested it.

So, after you get the life part. And no, life doesn;t consist of gaming, being emo, or slingy and etc. etc.

After you get a life, approach the woman with confidence or get her attention with it. Boast your best traits, but not too much. Show confidence and passion in your good hobbies and interests.

And just start chatting.

Then it will go naturally from there. Seriously, there's nothing to it. After you find out what she's like, you'll know if there's a spark between you two.

First of all, allow me to say that I can tell NOTHING from your picture. It appears smaller than one square inch on my screen.

To the rest of your question...

Striking up an impressive conversation with somebody you meet on the street would be hard, because you would probably not have much on which to base your decision to speak to her (that is, why choose her over some other random woman?), apart from her looks. Women who have little else going for them but their looks will appreciate you noticing their looks, but gals with a little something going on between their ears might be insulted. (I would.)

The bookstore is a little easier. It would help a lot in this scenario if you were both hanging out in the same section and could determine whether you have a common interest. Strike up a conversation where you get to show off your intelligence (not obnoxiously, mind you - you just want to prove that you have some), ask her questions (to give her a chance to show off her intelligence) and listen - REALLY LISTEN - to her answers. I have to tell you that there's a guy at work who is using this exact approach with me (the predominant subject is football, but based on my answers, or what's going on around us as we chat, he manages to ask other, personal-type questions that show interest but that are not overly intrusive, and then either asks questions based on those answers, or mirrors my answer back to me in his own words [this is referred to as "active listening"]), and although I'm not making any huge outward displays in response (as one of few women where I work, I'm watched very, very closely by most)...I have to tell you that he is turning me on beyond belief. This is all the more remarkable given the number of men who try to make an impression on me (more so at work, but also to an extent when I'm among the general population). He strikes me as being very sincere, intelligent and an excellent conversationalist, and he's clearly telegraphing signs of his interest.

In the grocery store, you've always got the produce section. Ask a gal who looks like she knows what she's doing in the produce section how to choose a nice melon/pineapple/whatever. Or you might take a recipe with you and ask her if she knows where they keep the ______ (fill in random ingredient from your recipe).

The bookstore is probably the easiest, I think. Or, you know, work...

Good luck!