You'll be able to begin this Stranger Mission, once you've completed the The Joys of Civilization Main Mission in Chapter 4. Head over to the northeast of Saint Denis where you'll find a guy who indroduces himself to you as the Professor, and he'll require you to fetch a good amount of Moonshine for him.
The Mercies of Knowledge Part II
You'll need to speak with the Train Station Clerk who is in Rhodes, head over to him and ask him if has any information on any large Moonshine Deliveries coming in.
The Mercies of Knowledge Part III
The info you recently gathered tells you that there is a moonshine delivery coming in from the north of Saint Denis, simply head over to the bridge and wait for the people to approach and use your Dead Eye to take out all the enemies. Once they've been dealt with, hop into the cart and take it to the Professor.
The Mercies of Knowledge Part IV
Upon delivering the Moonshine you'll find out that the Professor is building an Electric Chair, and requires you to find him a victim to test it out. Firstly, you'll need to head over to the Police Station and collect a permit from the chief which will cost you $100.
The Mercies of Knowledge Part V
After collecting the Permit head back to the Professor and let him know. Luckily he already has someone in mind to test out the Electric Chair, Wilson McDaniels, which you'll be able to find by heading over to his previous location that's shown on the Wanted Poster.
The Mercies of Knowledge Part VI
You'll need to travel up to the north to find Wilson in a camp with other enemies around him, quickly use Dead Eye to take them out and then hop on your horse and chase Wilson down and grab him with the Hogtie. Once you've captured him, tie him up and take him back to the Professor.
The Mercies of Knowledge Part VII
For the final part of this mission head over to the north of Saint Denis and watch the execution take place to complete it.