King and Rook vs. King; Elementary Theory
Basically, everyone knows the king and rook checkmate, but I am making this post for those of you who don't. I will show you in the following position.
Did you see the pattern? Every time the kings line up, white puts the checks the king forcing him back, but there are two things that you have to watch out for, which I will show you in this example.
No! A draw by threeway repetition was not what you were looking for, and your opponent is laughing, wondering what the heck you're doing. This time, I'll show you what you should do is that situation.
And so on until checkmate. If you are about to step in front of the opponent's king, just slide the rook over. Just as a footnote, watch out; don't let your rook get snapped off by the opponent's king.