What are the process I should take to get my partner who's on a student visa to get permanent residency in us

Assuming you are a U.S. citizen or lawful permanent resident, you will first need to marry. Once married, you may file an immigrant visa petition for your spouse. Your spouse may be able to file a contemporaneous application for adjustment of status to lawful permanent resident depending on your immigration status. You can read more about family immigration at http://myattorneyusa.com/family-immigration.