While times have changed and it's become more appropriate for girls to approach guys, some women still feel insecure or nervous about introducing themselves to a man of interest. However, with casual conversation and a sense of calm confidence, it's easier than you may think to strike up a conversation with a guy you're hoping to get to know.
Walk up casually to the guy that you're interested in with confidence. Try to hide any nervous feelings you have because that nervousness will come out in your voice. Smile as you walk up if you catch his eye.
Tell him something about himself, whether it's that he looks like someone you know or that you like his shirt and want to know where you can get a similar one (for your brother, of course). Smile and pay attention as he responds to your comment or question.
Touch his arm gently after he responds and give your response. For example, if you say to him "I love that shirt, may I ask where you got it?" and he explains where, you should laugh, touch his arm gently and say "Thank you, it looks good on you, I might get it for my brother's birthday." Give him a chance to laugh with you and comment.
Casually introduce yourself after his response and laughter. Hold out your hand and say "by the way, I'm xxx." He should introduce himself at this point. Do not let the conversation end there. Take your current situation into play with the next comment. If you're at a concert, ask him if he's seen the band before. If you're at a party, ask him how he knows the host. If you're in the office, ask him how long he's worked there. Ask a question that doesn't have a yes/no answer to keep the conversation rolling.
Try to throw a bit of yourself into the conversation as well. Mention something that you like or something that interests you to help him remember who you are in the future and to keep you on his mind. Don't hold him up for too long. Keep the conversation relatively short and end with a "nice to meet you, hopefully we'll talk again soon." Give him your number if you feel that he may be interested.