Learning checkmate in two is perhaps the most important step towards developing your fundamental calculation skills. Yusupov used this as a tool to improve the skill of calculating short variations in one of his books. There are various ways of teaching this to kids but what I am going to discuss is a multipurpose technique that is very effective.
I normally introduce this to kids once they show great accuracy in doing checkmate in one. I show them patterns first and explain fundamental ideas behind those patterns. It is advisable that you start with just a few pieces on the board first.
For example you can use checkmate with king and queen against king. If I am not missing anything, there are five ways to checkmate with these pieces:
The next task is to explain the basic idea behind this theme. In this case you can’t afford to allow the opponent’s king to leave the edge of the board (a-file,h-file, 1st rank and last rank) after which the rest is just matter of practicing it. Here is one example:
Here Black king will try to leave border line by moving to d7 so our first task is to prevent that. You can do it with Qd4, Qd2 or Qc7 (Qd6 is stalemate), so the king will be forced to move on f8 then Qd8 is checkmate.
Coaches have to find/compose lots of puzzles on separate themes. And yes repetition is the key thing as kids tend to forget patterns if they don’t practice them a lot.
You can add more pieces in order to increase the difficulty level but the basic ideas remain unchanged.