Hi everyone. I just need some help with a King and Rook vs. King ending. What is the best method to get your opponent's king in checkmate with this particular endgame?

Its pretty simple, given your rating you'll get the concept right away and only need it explained once, but it would be something of a pain to explain by typing.  Add me to friends, and message me sometime and I can explain it via demonstrating it on live chess. 

You should definitely learn it, as your rating is well past the point where just about everyone already knows that. 

There are techniques for executing the mate that allow you to proceed by rote. When to give check, king moving to long side, etc. But these are crutches. If instead you understand why king and rook can mate, it's really trivial to play move that lead to mate.

So here is some explanation and you can figure it out from this.

The king and rook checkmate the king on the side of the board (any of the 4 sides will do)

The king and rook push the opposing king to the side of the board in a similar way

Pick a side, force the king to move toward that side. Never let the king move away from that side.

You'll get a lot more out of working out how to do this, than some step by step instructions.

This is not the shortest way, but it is very sure, and it does illustrate the technique nicely.

Quicker, (but probably not quickest):

To try and put in more simply: 

(1) slide your rook up to whatever rank it can go to cut off the smallest part of the board with the king in it.  Think of the row your rook is in as a line of fire that the king cant cross.  You are going to advance that line of fire to cut the king off into a smaller and smaller part of the board (when you can).  The king is never ever going to be given the chance to cross the line of fire and get into the other part of the board.  Your rook only leaves the line of fire when it can advance the line of fire to cut the king off in a smaller part of the board.  The important thing is you have picked the line of fire, and the side of the board you are forcing the king too, the rook never leaves the line of fire until it can move up and push the line of fire closer to the edge of the board.   When you can, you move the rook up to advance the line of fire and force the opposing king into a smaller part of the board.  When needed you slide the rook along the line of fire to get as far away from the opposing king as possible so he cant bug you;

(2) the line of fire advances if he voluntarily moves back towards the side of the board you are forcing him too.  You can only force the line to advance when your king is opposite his king with a row in between you (the in between row is the current line of fire) AND its your turn.  At that point, you can advance the line of fire and his king must move back.

(3) you can never be the one to move opposite from his king, because then he just moves, and you dont have the situation described in 2.  He must move opposite you.

(4) to achieve this, you chase him.  If you are in the right row and one square to the left or right of him, and its his turn, he either moves (a) back, in which case you advance the line of fire; (b) opposite you, in which case you advance the line of fire; or (c) he slides away from you.  If he slides away, you follow.  When he gets to the end of that row, he has no choice but to move back or opposite you.

(5) if your king is in the correct row, one square to the left or right of his king, but its your turn, you dont move your king, you slide your rook one square along the line of fire.  Then its his turn, and your in the situation described in (4) above.

(6) when the line of fire reaches the 7th rank (or the 2nd rank depending on which side your forcing the king back too) (you can do this on the sides too obviously), then the king is confined to the 8th rank.  Checkmate is achieved by following the steps in (4) to force the king back a row.  Since there is no row for him to go back too, thats checkmate.

Yeah, its a mouthful in words.  Some of the diagrams above dont follow this most simple method, or dont go through it fully.  I like the diagram posted by E. Check, that one seems to follow this method.  Certainly there are shortcuts, but the method described above is the one you teach kids -- it always works, there is no need to get fancy when your learning. 

You can still message me to try it.  GL

That was the more simple way to put it?

I would go so far as to suggest that if you can't figure out mating with a rook from a few simple ideas, chess may not be the game for you.

I like the ideas in ArtNJ's comment. 

The strategy I use is just to get the enemy's king to a corner and then from there, checkmate is fairly easy. 

Use the rook to block the enemy's king off to one side of the board and then move your king over to protect your rook and to cut the enemy king off to a smaller and smaller piece of the board until it gets trapped at the board's edge. 

Once you get it trapped to the board's edge, move your rook (while still trapping the enemy king on the board's edge) until your king and the enemy's king is facing each other. If not, try to trap the enemy king into the corner. 

Little bit harder to explain but hopefully with the comments and visuals above, you'll get it. 

Checkmate!