Another way is to state the obvious, by saying, "Excuse me for stopping you, but I noticed you walking along and decided I'd like to meet you. I hope you don't mind my being so forward, but I believe that if you want something you should come right out and ask. Don't you agree?" All this should be said convincingly and sincerely. This should not be hard; it is the truth anyway.

If you get any kind of satisfactory answer, you can follow up with, "Anyway, my name is..., what's yours?"

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This type of approach can be applied with your “noticing the girl walking along" as she approaches you, and then with your speaking to her as you come together. But it also works very well if you let her get right past you and then double back, come up behind her, and make your approach. Sometimes you may not decide to make an approach until after she has passed. Don't worry, this is fine; you can go back and catch up with her. What you say is still valid – in fact it is even better. It allows some time lapse, and she feels gratified that she made such an impression that you had to come after her. The wording of your approach should be a bit different if you go back after her.

You should say, "Excuse me, but I saw you walking by a minute ago and I decided right then that I had to meet you. I hope you don't mind. ...etc." It often happens that she gives you a friendly glance as she passes which prompts you to go back after her. Then you can be sure she will welcome your approach. But even if she doesn't give you a glance of encouragement, you should still follow up if you are attracted.