In Game of Thrones Season 2, Episode 9: "Blackwater", Varys had this talk with Tyrion Lannister:
Varys: I don't believe I've ever told you how I was cut.
Tyrion: No, I don't believe you have.
Varys: One day I will.
Before that, they were talking about whether or not they believe in old powers, spells and curses. That leads me to assume it's somehow linked to magic. Does Varys ever tell Tyrion or anyone else how he became a eunuch in the books? And if yes, how did it happen?
I haven't watched all of the TV series, but as far as the books, yes it is discussed. It is in his wiki entry:
During their stay in Myr, a man offered a large sum of money for Varys, an offer his master found too tempting to refuse. The man gave Varys a potion that made him powerless to move or speak, but did nothing to dull his senses as his manhood was cut off at the stem, then burnt in a brazier in a Blood Magic ritual. Varys claims to have held a hatred for all things magical ever since.
He is telling this to Tyrion when they discuss the manner in which Lord Stannis has gained certain victories.
In the TV show, Varys tells Tyrion the same story in episode 4 of season 3, And Now His Watch Is Ended, after Tyrion asks him who arranged
the attempt on Tyrion’s life during the Battle of the Blackwater.
