First ascertain there is no ring on his/her finger. This is not a hundred per cent accurate, but it's a good starting point. You won't be as warmly welcomed flirting with a married person!

Avoid being creepy by coming off as genuine and not contrived. Explicitly sexual lines are creepy. Starting up a conversation based on the surroundings less so. Open ended questions are more likely to elicit a conversation than yes or no questions. Her response, if you are paying attention, will tell you what you need to know.
If she smiles and makes eye contact you're in! If she answers shortly, turns away or tenses up, she's not comfortable. Pushing it further will make things worse for you not better.

Giving her your phone number or email is less threatening than asking for hers.

Remember most women are genuinely flattered by the fact that you find them attractive. It's being treated like a sex object that turns them off. Women worry about being raped, if you are sensitive to this very valid fear you will do better. Don't suggest scary activities such as "come back to my place" to a complete stranger. Try having a conversation at first. People have to meet somewhere, a coffee shop is as likely a place as any.

One last caveat, if the person you are talking about is an employee be sensitive to the fact that she is a captive audience. She may not wish risking telling you how she really feels if her tip and / or her job is on the line.

I think the best place to meet someone, talk to them and eventually ask him or her out if it seems right is anywhere except a bar. I would never want to meet someone at a bar, because it seems that is the reason many people go to the bar. I know a lot of people only go to the bar to relax and have fun with their friends, but many people do go to bars for the sole purpose of being picked up, for a one night fling.

To me if one is serious about finding something for a meaningful, long term possibility of a relationship than talk to someone anywhere but a bar. A local coffee shop, bookstore, park, supermarket, etc are all fine places to talk to someone. I don't think people at those places are really looking for someone to date, but doesn't mean that you can't talk to them. Might find you have something in common with them and take it from there. Good luck!

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It is OK to do anywhere but in Church during service or at their spouses funeral. There are no rules for approaching someone you find attractive as long as they are not married, then let them approach you if you are single-this one is for guys. The only other place you need to be discreet is in an office that doesn't allow it. But there are no rules against walking up to someone and saying Hi, my name is...

Generally, I would think that there are no rules or limits to “pick-up spots”, if you will. I would hope that singles are free to make new encounters when and where they choose, as long as they go about the “acquisition” part tactfully. If individuals would not be able to talk to any single-appearing person they felt desirable, then many would never find their true match, their “soul mate”, as some might put it. Whether a singles bar is chosen to fulfill the purpose, or a more common, public place such as the library, a local café, or even a supermarket, I think all individuals should have the chance to try and meet the person they find most desirable and find out whether that person is indeed still available.