Students will see various things proven by contradiction, then they will practice applying the method on their own. Start the lesson by proving some basic theorems. Then ask the students to prove some basic theorems on their own. After that, show students Euclid's proof that there are infinitely many primes. Following that, give the classic proof that the square root of 2 is irrational, then generalize the argument to show why the square root of any prime irrational. Then generalize a bit further, to show the square root of any non-perfect square is irrational. Here's a quote I like, which you might show your students:

"Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game." —Hardy, A Mathematician's Apology