Flirting usually starts from a distance. This means your first flirtations are likely to be through nonverbal communication such as body language, a smile or eye contact. If you're watching closely, you will be able to tell if the object of your fascination is interested by how they respond to the signals you're giving.
Make eye contact with some measure of sensitivity. Instead of staring at someone until you make them uncomfortable and your eyes burn from lack of blinking, opt for a softer approach. Glance don't stare; allow yourself to look away every few seconds. When you catch each other's eyes once again, don't forget to smile. Also, if you're sitting with your legs crossed and arms folded, you are likely to give someone the impression that you're not interested.
Show someone you're interested by walking over to them first. Most everyone enjoys some attention now and then. Approach someone, and you flatter them with your courage and forwardness. Once there, the only thing you need to say is hello. You could use a million lame lines here, but nothing is quite so simple and open as just saying hi.
Start a simple conversation. You don't need to perform an extemporaneous speech on the advantages of socialism or anything, just talk about what comes to mind. It will be awkward at certain times, as it always is when meeting someone new. Roll with it when this happens, and let your laughter flow. By being able to chuckle during the awkward moments, you will be able to settle, relax a little more and begin to get to know someone. Lastly and very important, listen twice as much as you talk.
Don't Be Too Bold
Avoid coming in with a swagger. Nothing says "jerk" quite like the person who assumes they are a gift to humanity. A little humility goes a long way. This doesn't mean you need to shuffle your feet and speak in barely audible whispers while gazing at your belly button. As an alternative, remember that meeting people you don't know or having people approach you is a part of social living. Don't allow yourself to be overtaken by a fear of someone you don't know.
Bring a prop if you're in a setting where people don't generally break out into conversation. For example, if every day when walking down the same street in the afternoon you see someone who really interests you, perhaps saying hi doesn't seem appropriate. Next time, leash the dog, take the pooch for a walk and let Lassie be the ice breaker. Kids can sometimes have a similar effect as can interesting clothes, hats or anything else that draws the attention that you want.