Approach the girl, make eye contact and smile.
Initiate a conversation by saying something neutral yet friendly, tailored to your current environment. If the girl is a waitress or clerk at a music store, for example, you could ask her what food or artist she recommends. If she’s sitting in the park reading a book, you could ask for her opinion about it. Say something that invites a response and continued, worthwhile conversation, as opposed to a comment on her appearance or a generic question such as, «How are you?»
Gauge how the conversation is going by observing the girl’s body language and listening to her tone of voice. If she sounds bored and avoids eye contact, it is best to move on. If she sounds cheerful, smiles and makes eye contact, proceed with the conversation.
Introduce yourself by first name after a minute or two of conversation. Say «I’m John, by the way,» and extend your hand for a handshake. Chances are, she’ll shake your hand and tell you her name.
Ask before sitting down next to her, if she’s sitting at a table or on a bench. «Is anyone sitting here?» She might be waiting for someone else.
Offer some information about your day that you think she might find interesting, but avoid boasting. Talk about your classes, a movie you went to see, your job and your plans for the evening. Keep your tone of voice upbeat, and the conversation friendly. If you share about yourself, the girl will probably share, too. This way, you can find out if you have anything in common. You can keep this information in mind later, if you ever want to ask her to hang out.
End the conversation on a high note, before things get awkward. Subtly give the girl a chance to contact you in the future without pressuring her. If you have a business card, give it to her and invite her to call or email if she needs anything. If you are going to a community event later that you think she might be interested in, mention that you’re going. You might run into each other.
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