hello jos,
the trick in the quote can only be applied to very few boards and doesn't help at all with any other board.
there are a few general strategies though.
normal solving: solve like you would solve expert or genius level. hit f2 until an edge column or row of the board is solvable. use flags and clear safe squares. this is the easiest strategy but it is not very fast. it's best on big boards with medium mine density.
nf: hit f2 until an edge column or row is solvable but only clear the safe squares. it is fast on all boards that have fewer safe squares than mines. on big boards with medium mine density it might become a bit too difficult and other strategies might become faster.
blue face: once the number of of flagged mines is the same as the number of mines hidden in the board, the yellow face turns blue and a left click on it ends the board. if all mines are correctly flagged, the game is won, else lost. it is fast on all boards with a low mine density.
advanced nf - hexx-strategy: look through hexx' posts in this forum. he explained it very well in one of his posts. it's good on small to medium sized nf boards.
half-hexx: same as hexx-strategy but you only solve the opposite columns or rows at the start and then continue with rows or respectively columns. it is applicable to more boards than hexx-strategy.
advanced blue face: on some boards normal playing can't be beaten by other strategies, yet it can be optimized. once 90% of the board is solve, only flag the remaining mines. it can save a few seconds.
the key to fast times is knowing these strategies and finding the fastest for a specific board. often enough a few are equally fast and it becomes a matter of personal preference. this week normal solving, nf and blue face are about equally fast. that is, if you can execute all startegies equally well.
the best way to imrove is, obviously, to play a whole lot.