Politely Tell Someone if They Are Annoying

Is there someone you know who's annoying? If you want to be tactful about the situation, here's what you can do.

Steps

Think, "What annoys me about this person and is there anything I can do to change it?"
Think how you would like to be told that you are annoying.
Wait until you find the person alone. Tell them what about them annoys you and why. There is a good chance that they don't realize that they are irritating.
Gently remind the person when he or she exhibits the annoying behavior. If the person continues, he or she is either a)forgetful, b)malicious, or c)really trying to correct his or her behavior, but may not know the best way to go about it. You must then treat the person as what he or she is. The first two situations are not easily dealt with because there is nothing more that you can do. You cannot change a willfully annoying person or someone with chronic bad memory. If, however, your friend is sincerely trying to improve his or her behavior, remember to be patient. Nagging and complaining about this person's faults is not only counterproductive, it's also annoying to that person.
The most important thing to keep in mind is that no one of us is perfect, and treating your friends with respect and dignity is a priority. The Golden Rule ("Treat others as you wish to be treated") works well for this kind of situation.

If they are not guilty of 'major' annoyance, so to speak, it may be more effective to give some non-verbal sign that you are not happy with their behaviour, e.g. sighing, looking concerned. Of course, this depends on them actually being receptive to your cues.
DO NOT tell the person straight away "You're annoying!". It will embarrass the person and it will also hurt their feelings. Instead, tell them nice and calmly and explain to them what annoys you until they understand.
Don't give a lot of attention to the person when he/she annoys you
Be kind and gentle to the person. The more polite and reasonable you are, the more chance you have of being taken seriously.
With close friends, they may be joking. For them, tell them to kind of calm down. A phrase like "You're giving me a headache" will nearly always calm a friend down.
If the person KNOWS she is annoying (because most people tell him/her he/she is), but still doesn't change no matter what, you must be strict with her and tell her that if she changes, not only will people like her better, people won't go around avoiding/teasing her.

Don't tell them about this in front of anybody. This is humiliating. It can and will make the person angry and not listen.