Somehow in your development you lacked the necessary training of how to flirt or you may just need a refresher. First and foremost, a good self esteem is mandatory when flirting. Buy a new outfit, start an exercise program or get involved in an activity that boosts your self esteem. Feeling good about yourself will help you naturally attract others who feel good about themselves as well. Next, know what you are interested in. What do you find attractive? Take some time out and list those things for yourself. This will help you weed out the ones you really don't want and help you use your time more effectively. Next is eye contact, smile, and then talk.
If someone catches your eye do not look away. There's an unsaid Three Times Rule which says that if your potential glances back at you three times, he or she likes what they see. Smiling actually uses 13 muscles in your face so start working them out. Everyone looks better when they smile anyways and it helps ease the tension in the other person. Talking is an essential part if you want to succeed when flirting. The part of what to say is completely up to you and your personality. If you are not sure what works for you keep trying new things and eventually something will fit and work. You may want to try to engage the other person in a casual ironic or sarcastic conversation by making comments about mundane things such as the decorations or the ice cubes in your drinks. Make it something that both of you can continue to talk about and make it more than "yes" or "no" questions. Avoid topics like previous relationships, natural hair color, or your personal drama.
Another way is flattery. Comment on what they are wearing, their beautiful eyes, or their intoxicating energy. Keep it honest and light. Or just keep it natural and ask, "Having fun tonight?" or "What's up?" In any case, be yourself. The real you will eventually come out so if you want this to last longer than five minutes be yourself up front. Bottom line is if you see someone you like go up and tell them in your own way. Don't expect anything in return and keep at it. Persistence will be key in confessing your attraction to your desires and approaching the one you want. Over time this will help you cope with that paralyzing sense of fear of rejection and remember to not take things personally. The reason the person may or may not like you has nothing to do with you. They either like your type or not so go out there and start flirting already!