If the girl is waiting at a bus stop, in a line at a bank, or seated in a bus or plane, and you are similarly waiting or traveling, you can join her without even asking. But then you have to find a reason to start talking to her. This is usually not difficult. A request for help or any casual remark can be a starter. The weather, something she is wearing, or any well or any well-known current event will do the trick.

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Then casually say, “By the way, my name is…What’s yours? After all, you are both just killing time. If you have a long wait, everything should be fine. But if the waiting time is brief (5 minutes or less) you will have to arrange an extension of time.

A good idea is to ask, “Where are you going when you leave here? How about joining me for a cup of coffee?”

Another variation on the “waiting” situation is when the girl is seated with plenty of empty seats all about. Then, if you want to sit near her, you should get her approval.

You can say, "Excuse me, but do you mind if I sit here? I'd like to have someone to talk to."

But even better is, "Excuse me, but I saw you sitting here, and I decided I'd like to meet you. My name is ..., what's yours?"

Of course with all the “waiting" situations you don't have to be really waiting yourself. It is usually easy to join a waiting group to get near the girl. If you are really inspired by her, you might even take a bus trip you hadn't intended, though a plane trip might be a bit much.