How would one go aout traveling this route?
This is the website you'll want to use to plan the rail part of your trip, including that leg: click hereIt's a rail schedule website, you don't buy tickets on it. The date doesn't matter, but put 0600 for the time. And pay attention to spelling in place names but omit country names. That train ride is about 5 to 6 hrs, not including the time to get to the station, wait for trains, find your hotel at the other end, etc--it will be about all day.
From Interlaken, a local train will take you out to Spiez where you change trains to a high speed to Milan. From Milan, you take a local train to Varenna. Depending on the train run, you could have an extra train change in Brig. You can easily buy the tickets for your departure when you arrive in Interlaken.