How to get from Providence/Stoughton train line in South Station to Alewife subway line?

Take either Braintree or Ashmont, and get off at South Station and the Providence trains leave from there.

I understand your question. When you get of the train at South Station, the trains will be on outdoor covered platforms, so you walk toward the building, just follow the direction that most people will be walking. When you enter the South Station building you'll be in an area like a food court. Walk straight ahead until you see a set of stairs going down (there will be a restaurant/ bar right there) go downstairs and you'll come to the MBTA red and silver line. In that area, buy tickets for the RED line. Then go through the turnstiles and you'll come to a set of stairs. Go down the first set and turn RIGHT to go to Alewife and go down ANOTHER set of stairs (so you're going down stairs TWICE, bcuz the first landing is for the silver line which is not what you want) the 2nd set will take you down further and that will be the red line, Alewife train. Hope that helps! Welcome to Boston! =)