One way to learn this ending is to add a rule for yourself: Never put the
opponent in check, until the final mate.

You'll have to use the double-wall method. For example, with the R on d4
and the opposing K anywhere in the rectangle e5-e8-h5-h8, the opponent is
walled in (to the upper right corner) both horizontally and vertically.
Move the R only when it tightens the wall, i.e. reduces the opponent's
available area. In this case you'd move the R only upward and rightward,
never downward or leftward, and never more than one square at a time -- and
never check the opponent. Whenever your R has no such move, move the K --
keep the R defended -- and wait for the opponent to yield a square.

This may not be most players' method with this ending, but I think it's the
most instructive.

Bill Smythe