For what it's worth, my suggestion (as a woman) is to not launch straight in with something about how attractive you find her, even if you intend it as a compliment, i.e. "Hi, sorry but I couldn't stop thinking how pretty you are" or "Wow you have lovely eyes" etc.
It immediately puts me on my guard as it's very apparent you are now trying to flirt with me.
This may seem counterproductive if you're a guy (you want to let a woman know you're flirting, right?) but launching straight in like that is both intimidating and, unless you're particularly good with words, actually comes across as faintly creepy. You may be being genuine telling me I have nice eyes but all I hear is "Hello I am a total stranger and I've been staring at you intently for the last half an hour and now I wish to let you know this in the hopes we eventually have sex!"
For me personally, I would say a few top tips are:
- Read the situation; if I'm with a group of friends or am actively chatting to someone else, don't interrupt and don't just come and sit down at my table.
- Being chatty and friendly goes a lot further than launching straight in to a pre-planned 'cheesy chat up line followed by compliment' duo. Just make friendly small talk and see how she responds (if you get one word answers or confused smiles, she isn't feeling it so bow out graciously)
- Don't 'crowd' her - nobody appreciate being cornered by someone trying to flirt, so standing right next to her at the bar, leaning in to her putting your arm agaist the wall next as though 'blocking' her in etc are just crappy things to do.
- I feel like this needs to be said (so I'll expect the neckbearding hate to follow) but it's also the best advice I can give any guy in this situation, She is under *no** obligation to appreciate you're flirting with her. It's a hard truth to accept (for me *and women trying to flirt) but there's a possibility she won't be feeling the attention and will try to let you down. If you get rejected, it speaks volumes about you as a person if you graciously accept that you tried and that it didn't work. A simple "Well it was great chatting to you, enjoy your day/evening/etc" folllowed by a smile will not only help your own self confidence but not mark you out as "that guy who doesn't take rejection well" to other people in the bar.
This isn't intended as anything other than friendly advice on my part. AskReddit often gets questions like this and the answers I've seen can sometimes be a little....sketchy... so this is just my personal opinion based on my own experiences.