So the story's in the paper, but it's wrong. It's not the truth as you see it, or there is simply a fact, perhaps a date or name, that is incorrect. Get a hold of the right person, show that you have a valid case for complaint, and the newspaper may print a retraction, admitting and correcting the error. But remember to remain professional and pleasant along the way.
Examine the story closely. Decide if the truth has not been served in the story (in your view), or if you think there needs to be a clarification of the case made public.
Contact the desk editor or metropolitan editor if the story refers to a local news event. An email address or phone number should be on the newspaper. Check on the opinion page for newspaper publishing details.
Keep your demeanor pleasant and appreciative when talking to the press staff. Thank the editor for printing the story. You may be miffed, but the editor may think they did the right thing. Then explain your position clearly and calmly. Detail how you feel the story should be written or how something should be phrased and why.
Ask to speak to the reporter if your issue relates to a local news story. The reporter who responds can better explain her reasoning, and she may also lead you to her source of information, whether police or highway patrol or firefighter. You may then call the police force, for example, and ask who handled the case. Sometimes facts are claimed before an investigation has been made and before a police report is even filed. So things may still be in question when a story gets written, but the story should reflect this and not claim unproven facts.
Get a clear idea of whether the newspaper will print a retraction or not. If an editor responds favorably to your phone call or in-person contact (better than email), he should give you an idea of when the retraction will be printed--usually in the next few days. Check to make sure this actually happens.