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This is very corny but it always works for me.
During the conversation, I make a surprised look and make it obvious that I'm looking at her eyes.
Interrupt the conversation by, "wait, I just noticed how beautiful your eyes are that it could mesmerize me"
The eye contact thing is correct, but I wouldn't recommend so openly announcing such an obvious compliment when you've only just met a girl, especially a really common one she has heard a million times before. Stare into her eyes while she is talking, from one eye to the other, without looking away. The key thing with eye contact is NEVER be the first one to look away. The whole point of eye contact is to build up awkwardness. The tension of awkwardness is good because eventually a girl will want to break the awkwardness, either by looking away (i.e. playing hard to get) or by kissing you.
Apart from eye contact, you need to touch her within the first 10 seconds of introducing yourself and keep up the touching as much as possible, during the conversation, that way it won't be weird or creepy when you start touching her more intimately later in the conversation, because you've already buttered up her comfort zone by touching her early in the conversation, so she is anticipating your touch and is relaxed abou it. Once you notice her looking back into your eyes and holding your gaze, it's on. Look at her mouth a lot and go in for the kiss.