I'm a us citzen and so is my wife. My wife's family lives in south korea and her niece would like to come here to go to school. How do we start the procees right.

Find a private school here for her, get the FSA to issue a SEVIS I-20.

With that, have your niece apply for the F-1 visa at her home consulate. Will need to show that the family has funds to pay for her schooling and expenses. She must show she intends to return home. No dual intent allowed for F-1 students.