Research the law in your state or seek professional assistance. In some states, you might need to publish notice of the name change before you file a petition with the court. In other states, you first file the petition with the court and then file notice of the name change. In most states, you need to publish the notice multiple times over a set time period.
Ask the clerk of the court in your county if there are any specific newspapers in which you should publish. Different states have different rules. The general rule is that you need to publish in a newspaper of general circulation in the county where you live.
Call the classified advertisement department of the newspaper and ask for its procedures. Newspapers that offer the service normally have a set way of handling it. You might only need to give the classified department the basic information and the employee will know what to do.
Pay the newspaper's fees for publishing the notice.
File your state's notice of publication with the clerk of the court after you have published the notice the appropriate amount of times in your state.