A genuine compliment will suffuse the recipient with positive feelings, and oils the wheels of social intercourse. Only offer genuine compliments . Don't over-compliment - you will look like an insincere flatterer.
Stick to specifics; vague, over-generalised compliments are easily devalued. Try to keep compliments appropriate to the context and remember that specific beats general. A compliment on a haircut or dress will be much more appreciated that a generic and unimaginative ‘You are looking well’.
Never damn with faint praise, or give a compliment with one hand and take away with the other; "You look great - have you lost weight?" is a classic example of the double-edged compliment (only appropriate if the recipient has openly acknowledged a weight problem/diet etc.). Try and give the compliment in a timely manner; don't wait until you are leaving a dinner party to praise the food, for example, do so when you first taste it. A spontaneous response always feels more genuine.
If someone pays you a compliment, smile and thank them graciously, and do not demur. Try to avoid the British and very female – ‘Oh this old thing’, a form of self deprecation which can make the person paying you the compliment feel they have done the wrong thing and dent their confidence.