Under FEDERAL law, which applies in all states- you must be 21 years of age, not have been convicted of a felony or crime of domestic violence, or under indictment for same. You cannot have been adjudged mentally incompetent, be an illegal alien, drug addict, have renounced your citizenship or been dishonorably discharged from the US military. Purchase must be made from a dealer in your home state (or transferred through one).
STATE law- in addition, there is option 1 or option 2. See link: https://dps.mn.gov/divisions/bca/bca-divisions/administrative/pages/firearms-permit-to-purchase-transfer.aspx