In a speculative approach you ask questions and expect the girl to give answers or discuss a subject. You are conveying the impression that you really are interested in finding out something and that was the reason you approached her. In some cases you appear serious in your interest. In others, your interest is not to be taken too seriously; it is merely a play to start a conversation and you expect her to recognize this.
Examples:
"What do you think of...?" (You are in a "waiting" situation with her. Any
good topic is suitable. It helps if you are reading a newspaper or magazine.)
"Hey, you must be tired from walking around so much. Why not sit down for a spell and tell me what you've been up to?"
"Are you a dancer? You move like one." (Quizzical look while asking; but only use this if she, in fact, moves gracefully).
"Hey, where are you rushing off to?"
"I see you are a ..." (or "I see you have ...") Refer to some feature about her which should require some additional explanation from her. We have already mentioned the use of this type of line in a casual way. But in this situation we mean that you should use the line more as a question that really requires an answer.