Last night I went to starbucks coffee. I found a lady who was studying English. I supposed she was over 30 from her appearance. She was alone. I went to her, and said "Hi". She lifted her head, and asked, "Do you have anything to do?" Then I didn't know how to answer, uttered "Nothing". I really didn't know what to say at that moment. I found it was not fun, and stayed around for a few seconds and left the coffee shop. If I meet the same situation next time, what should I say? How should I act? I think it is quite a typical scenario. Thank you.

There are 1000s of things to say and do... just do not freeze...


examples:
She: Do you have anything to do?

you:"Right now I'm just figuring out if the search for the girl of my dreams is over"
you:"Not really and you look friendly and cute so I decided to come and talk to you"
you:"Yeah I guess so but what could possibly more important than talking to a cute girl like you?"
you:"I was supposed to avoid a bank from being robbed, but I forgot my spider mask at home so now I better spend my time talking to you"

There are really a lot of ways to reply, just be proud of your decision to start talking to her, and your intentions of wanting to meet her... there is nothing wrong with it... do not hide it.

Worldrunner, the examples you gave are really great. But after that, what else can I say?
For example:
She: Do you have anything to do?

me:"Right now I'm just figuring out if the search for the girl of my dreams is over"

She: ^_^
Me:... (what else can I say?)

"I'm ___, what's your name?"
"This is a nice place, do you come here often?"
"You've an interesting smile, are you a lawyer?"
"So besides picking up guys in Starbucks, what else do you like to do?"

Just have in mind 3 different things to ask, usually if after 3 questions the conversation does not spark to a point where I do not have to be thinking anymore what else to say... then I consider it a good time to retire...

Tip: the questions work much better if they have a little statement at the beginning, and at the beginning of a conversation I've seen that it is better to ask simple easy to answer questions than very open ended ones... I've seen that when people is still not comfortable with each other, these big personal open ended questions usually freeze the other person's mind, and they end up answering something short and meaningless.

These is what I've learned that works for me in order to start a conversation... I guess there are lots of ways to do it.