There is a right and a wrong way to give compliments to girls. In fact, there is a way that is very very right, and a way that is very very wrong.
Some guys will tell you not to give compliments at all, but giving compliments can be a very powerful technique when done right.
The wrong sort of compliments come from a place of perceived lower value.
This is how AFCs compliment chicks. They say "You're so pretty" or "You're so clever" and the subcommunication is "I hope someone like you could be interested in me!"
Conversely, proper compliments actually subcommunicate higher value. They should come from a position of authority and imply a unique quality or commonality.
The proper structure for an effective compliment is:
1. Compliment "that's a great scarf"
2. Qualify the compliment "it matches your mascara and shoes, I like that"
3. Challenge her or enquire "did you choose it yourself?"
Thanks to Geoff of RSD for educating me on point 3.
1. "You're very confident... I like that in a girl... How did you get to be like that?"
2. "Nice dreadlocks!... They must have taken ages... Aren't they hard to clean?"