Article II, Section IV of the Constitution spells out how someone can be impeached:
"The President, Vice President, and all civil officers of the United States, shall be removed from office on impreachment for, and conviction of, treason, bribery, or other high crimes and misdemeanors."
Read more about some actual impeachments:
Impeachment of Bill Clinton- (President) Acquitted, stayed in Office
Impeachment of Alcee Hastings- (Federal Judge) Convicted, removed from Office
Impeachment of Andrew Johnson- (President) Acquitted, stayed in Office
Impeachment of William Blount- (Senator) Dismissed, expelled from Senate