If you're out and about during the day, and you see a girl who you think is hot, just approach her, even if she hasn't given you eye contact. If she is giving you EC, it just gives you a little bit more of an incentive to approach - bonus. Just think to yourself "What's the worst that can happen?" tell her that you think she's cute and ask for her number.

Regardless of how the approach/interaction goes, she should be flattered that she's been approached by a guy who isn't under the influence of alcohol, and you should feel good about yourself for doing something that the vast majority of guys never have the cojones to do.