When the word didactic is used, it is typically referring to one's style of teaching, or instructing other people. Beatty is an interesting teacher, who employs interesting didactic methods to "teach" Montag. There are a few key words that I would use to describe Beatty's didactic methods. I'll list them below, with examples.
1. Aggressive and threatening. Beatty, after Montag returns to work at the end of section two, nearly attacks Montag, aggressively quoting book after book at him, to make the point that books can be used to serve anyone's argument, no matter what it is. As a result, books are "traitors." Beatty wants Montag to learn this lesson, probably because he has felt betrayed by books himself, and because he wants Montag to drop his pursuit of books and conform. He knows that Montag is hiding books (Mildred and her friends alerted him to that), and is upset that Montag has chosen this path. So, he aggressively stuffs the lesson that books are worthless down Montag's throat, in a pretty threatening way.
2. Logical, and sarcastic. When Beatty comes to Montag's house to lay out the history of firemen and book burning, he is pretty open, frank, and inclusive. He logically lays down the facts for him. He presents the history with many, many details that help Montag to understand how they got to where they are today. He sarcastically puts himself into the shoes of society and how they have responded to each event with such offense, laziness and outrage. He uses that sarcasm to point out how things progressed, and to point out the rather illogical and silly ways of people.
3. Subtle. Beatty likes to drop hints that alert Montag to the fact that he is aware of Montag's curiosity with books, and that he would like him to expore it briefly, then get back to normal. At the end of his history lesson, Beatty hints,
"Well, then, what if a fireman accidentally, really not intending anything, takes a book home with him? A natural error. Curiosity alone...we let the fireman keep the book twenty-four hours."
Here he is letting Montag know that he knows what is up, without directly stating it. He is teaching a valuable lesson: I'm on to you. Satisfy your curiosity, then get with the program. Beatty later admits to sending the hound to Montag's door to indirectly scare Montag into stopping his quest.
I hope those thoughts help; Beatty's an interesting character with a dynamic teaching style. Good luck!