To file for divorce in Minnesota you must file a Summons and a Petition for Dissolution of Marriage with the Clerk’s Office of the county court. Although the exact filing fee will depend on the county in which you file, Minnesota has some of the highest in the nation with the average around $400. Whether or not you are representing yourself, you must also file a Certificate of Representation.
A trickier question is whether you may record the other parent's conversations with the children. Under the doctrine of "vicarious consent," as long as a parent or guardian has "a good faith, objectively reasonable belief that the interception of telephone conversations is necessary for the best interests of the children," then he may consent to the interception (i.e. listening in or recording the call) on behalf of the children.  However, this can be risky, because if there is any dispute about whether your vicarious consent was in good faith or objectively reasonable, you may still end up having to defend against possible criminal charges or a civil lawsuit. The Wagner case I have cited, for example, was a civil lawsuit by a one parent against the other parent who had recorded telephone calls between the children and herself. The Court allowed that lawsuit to proceed because there was a genuine issue of material fact as to the motivations of the parent who had made the recordings. I don't recommend recording any such phone calls without first consulting a lawyer.
A divorce can get complicated if the parties have property (real estate, automobiles, vacation property, pensions, jewelry, etc.) or minor children. Usually, the divorce can be done more quickly if the spouses agree on how to divide the property and handle custody and parenting time with the children. Many cases start out with a lot of disputes, but then the parties are able to reach an agreement. Parties often reach agreement after using alternative dispute resolution (ADR) services outside of court. NOTE: If you feel threatened by or unsafe with the other party, you may want to get legal advice or help from an advocate before using ADR.