You should register to vote from the address you currently consider home. For many students, this is likely a school address or a parent's house. If you still go back to visit but no longer consider it your home, then you should register to vote where you live at school.
If you moved to Minnesota from another state and currently consider Minnesota your home, you can vote here even if you pay out-of-state tuition or have a driver's license from another state.
If you do not consider your school address to be your home, you can apply to vote by mail with an absentee ballot. Minnesota voters can apply online; otherwise, visit your home state's election website.