Guttorm is listed in Digitalarkive for May 9 1872 on Tasso, Agent: Hansen. From the date it seems probably he traveled from Hull to Liverpool to New York, then on to Goodhue Co. MN.
How do I determine which ship he would have taken to New York? Using the Agent info and date, it seems as if he would have been on the White Star Line, perhaps on the s/s Adriatic leaving May 16th. How do I determine if this is accurate? How would I find out how he would have come from New York to MN?
I agree, the Adriatic looks like the most likely ship. The only way to determine if he arrived on that ship is to check the actual passenger list (arrival to new York 1872-05-25). You can find more information about how to get access to US passenger records by reading the article US arrivals - Customs Passenger Lists . To find out how they made it from New York to MN is more tricky. What you could do is to read old newspapers to se if they have notes about train or steamboat conectoions and departures or maybe adverts for inland voyages. Then can guess how they most likely traveled. The old New York Times archived newspapers are online and can be accessed for a fee. They can be searched for free, but if you want to load the content you are asked to subscribe, however, it is really interesting reading.