Hi.
I have to admit - I was always pretty lousy at flirting for the purpose of showing my interest in someone.
I think that flirting is okay if it is done respectfully. Smiling, eye contact, exchange of pleasant words (e.g. that is such a nice colour you're wearing. It brings out the blue in your eye." All of this is okay. It doesn't have to lead to anything (exchange of phone numbers or ???). It is just that - pleasant social exchanges.
I learned (through a LOT of trial and error) that the best way of approaching someone after an exchange of pleasant flirtation is to do the following:
1. Look for a wedding band or engagement ring (I know I know - a lot of people are in committed relationships and are either not married or don't wear a ring - however, it is still a good first sign). If a wedding ring is being worn - it really is just simple innocent flirtation. Enjoy it for what it is.
2. LISTEN - in the course of conversation, the other party might refer to a significant other (my boyfriend/girlfriend; my partner; "us" "we"). If they refer in any way to a significant other - again, enjoy the flirting as an innocent diversion.
3. If you really are interested in the flirter and there are no signs of them being in a relationship with someone - bring up some topics of conversation to share. Mention your love of a local coffee shop's biscuits or a your favourite flavour of Bubble Tea. Have your phone number or business card with social contact handy and offer it to the flirter. Say, "If you ever want to talk more, I'd love to join you for a coffee (or whatever your beverage of choice is) at the local coffee shop."
By doing the step in #3, you are not putting them on the spot (e.g. you're not asking them for their contact info - which they may not be comfortable giving). Also, it is a friendly, non-intrusive invite - they can call or not. The only caveat - DO NOT SIT BY THE PHONE WAITING FOR A CALL. Remember, this is all fun, casual flirting. There is no obligation on anyones part to move this forward. Even if the flirter takes your number - they may just be taking it to be polite, but have no interest in calling. Don't take this as a personal slight. If they take the card, say again, "Please feel free to call, it's been delightful speaking to you." and move on. The flirter will make the next move (or not).
Maybe the flirter will say, "um... I'm not interested" and hand you back your card. No worries, your next line is, "that's okay - in any event it was delightful speaking to you. Take care," smile and move on.
In any event - you will have conducted yourself with poise and grace and had some fun with flirting.
Incidentally - just a little about myself - I am married with two kids. I was lousy for the longest time at flirting (it doesn't help that I will never be mistaken for a model LOL
) I did meet my dear husband at an online dating site. This way - it was pretty obvious that we were both interested in meeting someone - had a chance to see each others picture and chat on-line, on the phone and then meet. It took a lot of the guess work out of the process for us. 