just order a drink,get it sent to her,and tell the waiter to point you out and say he ordered it for you. look at her while she receives the drink,if she smiles,then go over to the table and start a convo,if he gives you a weird look(like a go fuck yourself look),then save yourself the embarassement.
If she smiled,that should ease things up a bit. go over,greet her,ask her for her name,then ask her what she does,say its interesting,crack a joke(short one,like a one liner),then if she laughs then you might friend hit the jackpot. Once you get her to laugh,then you're in the zone.
After that ask her, what is a beautiful women like you doing sitting all alone in a bar. She will give you a reason,maybe she's sad. comfort her and shit. If she is single she will most likely like you and want to exchange numbers, or if she's a whore she'll invite you over for some sex.
if she's a whore,fuck her then get the fuck outta there never to call her back.
If she's a respectable woman then its all good.
hope this little guide helps the n00bs.