The Knights of the Mind is a quest. It consists in delivering a letter from Septon Garibald to Archmaester Harodon in Oldtown.
Starting the Quest
Attention: In order to start this quest you must have A New Beginning active or completed, as this is the only way to talk to Septon Garibald without him saying he's busy.
Talk to Septon Garibald and he will give you the quest item Garibalds Letter, which he asks you to deliver to the archmaester Harodon in the Citadel.
Traveling to Oldtown
The Citadel is located at the city of Oldtown, which is at the southwest corner of Westeros, west of the Dornish mountains. Make your way there, the easiest and most obvious path is through the reach, take care with the bandit groups as they can be really hard to beat early in the game.
Once in Oldtown you can visit the Citadel, there are two places to go, the Seneschal's Court and the Archives. I recommend exploring the Archives first, as there you can talk to a maester and acquire the Book of Patrons as well as talk to an acolyte and learn that Maester Yandel in the tavern might have work for you. Also inside the Archives you'll find Archmaester Castos who'll give you the quest Lost Knowledge. Near the Archmaester there will be a chest with skillbooks in it, you can take them with no consequences.
After you're done exploring go into the Seneschal's Court and talk to Archmaester Harodon and give him Garibalds Letter. He'll be unimpressed with the letter and at some point will ask you if you believe in the Seven Gods, you'll have to make a decision:
If you answer Yes I do. You'll get +5 relationship with Ser Baelor Hightower.
If you answer I do not. Nothing will happen.
After giving him the letter the quest is completed.