Although by definition a motion for reconsideration asks a judge to reconsider a ruling he made in a court order, the laws in almost every state prohibit filing one just because you disagree with the judge's opinion. A motion for reconsideration usually can only be filed if the judge made a factual mistake, such as using the wrong income for a parent in child support calculations, or if he failed to consider pivotal evidence. It's not an opportunity to retry the original motion, and almost invariably the motion goes back to the same judge who heard your matter the first time.
Go to the courthouse to purchase an audio recording of the initial hearing. You will need to cite the judge's specific words regarding the part of his order you think is in error, especially if he explained his reasoning. Have a transcript made of the recording so you can use the written pages as an evidentiary exhibit, if necessary. However, in most states, you can only use transcripts prepared by a court-approved transcriber as exhibits. Don't listen to the recording and type the transcript yourself.
Prepare a certification, explaining in writing why you think the judge erred. If he made a decision that contradicts your state's statutes, you will need to quote the exact statute. If you can find an example in case law where another judge decided a similar matter differently, cite that as well. If the judge made a factual mistake, explain why and support it with proof. For instance, if he used the wrong income figures in a child support calculation, attach copies of tax returns giving the correct income. If applicable, attach the transcript pages well. Sign the certification and have it notarized.
File the notice of motion and your certification with the court that heard the original motion. Serve your adversary with a copy immediately, either by process server or by certified mail. All states have requirements as to how long you have to accomplish this after you receive a signed copy of the judge's original order, the one you are disputing. As of 2011, in New Jersey, this time period is 20 days, but in Hawaii it can be as short as 10 days and in Arizona it is only 15 days.