On the west side of Clintville is a man standing in front of a small building with a hat like the man in the tile for this achievement. Talk to him and ask him about his hat. Keep talking to him and he will eventually mention wanting a train ticket from a specific date in the past.
Now go South one screen and then East one screen to Clintville Station. Go inside the train station and talk to the Ticket Salesman behind the counter. Ask him for a ticket, and then tell him you want a specific ticket and he will eventually give it to you. Now go back to the original man and talk to him and you will give him the ticket and he will give you the hat. This will unlock the achievement.