What's the best way to approach a girl in a club?

The best way is to start random conversation. Walk past and ask a random question, or walk up to someone she is with like her friend and ask them something. You can ask a question like-"what time does this club close down?" You will definitely get a reply and you can add your inputs or views to the reply.

Since women are used to getting approached by men, the best way to approach them is to not let them feel that you are trying to hit on them. Once they know your real intention, they will not pay attention to whatever you say or in other words, they will put a wall around themselves.

So the typical idea of walking straight at her, introducing yourself, handshaking, asking her name, telling her yours are all going to activate a defense mechanism.

If you want to approach a woman who is in a mixed group of men and women, it is always a good idea to talk to the guys first. This will help break the ice with the group.

After you've talked to the guy for a moment, simply ask everyone, "so how do you all know each other?" A lot of the time they'll be co-workers or the woman you're interested in will be somebody's sister or cousin. And if she says she's so-and-so's girlfriend, then you simply smile, say "great meeting all of you!" and walk away.