I don't know how to cultivate affections in a systematic way, but much of it seems to come from exposure, experience, and imitation. Kids can't love what they don't know anything about, so if we want them to have affection for the cardinal virtues, or theological virtues, or the fruits of the spirit, or the beatitudes, or great literature, or mathematics, or whatever, then we have to expose our students to those things. Exposure isn't enough, however. It must be meaningful. It must be woven into an experience that either a) captivates, or b) cultivates, or both. Captivation seems to come from beholding beauty (which stirs adoration and admiration) or sublimity (which stirs humble fear and awe). Cultivation seems to come from consistently repeated habits. Captivation seems harder to manipulate, whereas habits can be trained through careful ordering of practices. For example, do I want my student to love good penmanship? Then I have to make him write and rewrite paying careful attention to the way I place the paper, the way I hold the pencil or pen, the way I make the strokes, etc. all the while praising the beautifully done aspects, cheerfully correcting the poorly done efforts, and faithfully rebuking the slothful efforts. The demeanor of the instruction just mentioned leads into imitation. Whoever is leading the students' cultivation must herself exhibit what she would have her students learn. I'll admit that this is where I have the most trouble with my own children, because of my selfish impatience for them to "get it right the first time."
I don't know if these thoughts bear out the truth, or if I am missing something or am mistaken in some way. If only Socrates were here to test these thoughts, or I had some way to see how students who have been given these things have turned out, I could have more confidence in their success!