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Step 1
Ask a (sober) and good friend of the annoying party guest if their friend would politely leave. Don't be melodramatic or passive-aggressive. If the friend has any sense, and you asked in a completely polite way, they will see the reality of the situation and take the annoying party guest away with them.
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Step 2
Have a "high value" friend ask the annoying party guest to leave. This should be one of the people at the party who is very self confident, not passive aggressive, and not easily excitable. When asked to leave a party, a person will respond much better to a cheerful, dominant person than anyone else. The person being asked to leave may not be aware of the behavior, so it's best not to scare the person into being defensive. Pick a friend who is very outgoing and without a mean streak to be your bouncer.
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Step 3
Cut off the annoying party guest. Sometimes, an annoying party guest is fueled by alcohol. Serving that person more alcohol will not help things. Firmly but kindly cutting off the annoying guest may result in the best possible situation for everyone involved.
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Step 4
Be firm, but don't be overly dramatic. Sometimes parties are so stressful that unneeded drama can rise around the presence of annoying person. Keep it in perspective. Threatening the annoying person in any way, even with calling the police, can bring huge amounts of tension to a party, even going so far as to make you look like an inconsiderate host or hostess. Be very careful that you don't overreact to someone's behavior.
