In a club scenario, you will first want to identify someone you are interested in. You will want them to look comfortable in their environment --- chatting loosely with friends, etc --- so that they will be more receptive to your flirting attempts.
When you are ready, focus on the target of your attraction and move across the room towards them. Move confidently but not too quickly. When you have gotten close enough, reach out with your hand and introduce yourself with a simple "Hi" and your name. As you introduce yourself, make sure to make eye contact with them in cycles; eye contact for 2-3 seconds, then looking away casually for 2-3 seconds.
When shaking their hand, allow your hand to linger just a moment longer than usual. This will get their attention right away and let them know you are interested. While in the midst of the hand shake --- and as part of your bolder move --- look them up and down as slowly as you can muster and return your eyes to theirs, smiling.
After your introduction, offer a quick compliment or joke. Take advantage of a loud room by leaning in and whispering the compliment or joke. If they have tattoos on their arms or are wearing a piece of jewelry or an article of clothing that appeals to you, make this a part of the compliment to show your interest.
Take it a step further by making body contact with them in the form of touching or brushing the clothing, jewelry, or tattoo they are wearing. If they smell nice, lean in and mention that they smell great, perhaps asking them what perfume or cologne they are wearing. Physical contact is considered a very bold move and will let you know right away if they are accepting of your advances.
During the resulting conversation, keep the topics light and positive while making it a point to divert your target away from their friends. There are two ways to do this. If you are at a dance club, find out if they like dancing. Take them by the hand and ask them if they would like to dance. If you are at a casual bar, ask them if they would be interested in finding a quieter place to talk.
There are some other extremely bold moves you can make in certain situations that may just win you your prize. If you are leaving a club quickly --- due to your friends or other circumstances --- but are interested in someone, then write your name and phone number on a piece of paper and approach them. Introduce yourself quickly, shake their hand and lean in, complimenting them. At the same time, take their hand with both of your hands and slide them the piece of paper with your name and number.
Take the compliment to the next level, saying you have to go but think they are beautiful or handsome and to call you because you would like to talk. If they are familiar with your group of friends, you may even go as far as to ask them to come with you as you hop to the next club.
Bold Flirting Warnings
While bold flirting may get you everywhere -- and can be fun, as well -- understand that it also can get you into trouble if you are too physical with your advances or if you fail to see the other person simply is not interested.
It is always better to ask before you take it a step too far.