I tended to do The Look with strangers (say at a bar or similar). It has worked a treat in the past, and basically my ability to do this has led to much more success in the dating world than I otherwise would have had.
From http://community.sparknotes.com/2010/01/05/auntie-sparknotes-how-to-flirt-part-1-the-look:
Quote:
Most of us just aren't comfortable walking up to a cute stranger, out of the blue, and saying, “Hi, what's your name?” (If you are, you probably don't need this guide. Get out of here.) Fortunately, there are other ways of initiating contact with someone you're interested in. If you don't know your flirtee (or don't know him well) The Look is the first way to signal your interest—and also, to gauge his interest in you.
To catch somebody's eye from across the room—in class, at the pool, in jail, wherever—try to let him catch you looking at him. Every so often, allow your gaze to drift over the room and settle briefly on your flirtee. If he looks back at you, meet his eye for just a moment—about as long as it would take you to quickly say the word “Mississippi”—smile a little, and then break the eye contact and look down.
With people I actually know, I've tended not to do much due to being too self-conscious. Similarly to Beau, I would blush more around them. So rather than doing deliberate actions to attract them, I'd try to ask them out on a date-like activity, where I could feel more comfortable being flirtatious.