I am relatively new to chess, and wonder, what is a fast (and hopefully easy) way to learn chess board coordinates, so when I am watching a video where the commentator says 'Knight F 6' ,i know to look quickly at f6, and i don't waste time looking for coordinates on the edge of the board, or count it.
Some websites offer "coordinate drills". I'm not sure how effective they are for learning, but you can certainly give them a try. I found it to be surprisingly entertaining to try to beat my personal record number of coordinates per minute (or whatever the time limit is). Here are the two I know of, but maybe there are others (and maybe there are apps, as well):
Personally I've found that studying openings (and to a certain extent, checkmate patterns) helps learn coordinates because you start associating coordinates with certain moves, which gives each square its own "personality". For example, c4 is not just c4 anymore; it is the square where the bishop goes in the Italian game, or where the pawn goes in the queen's gambit.
This is something that you gain through experience. One good way to obtain that kind of experience would be to buy a large game collection - for example, a modern algebraic edition of the 1953 Zurich tournament book by Bronstein - and play through them. Not only will the experience accustom you to finding each square, you'll undoubtedly learn something from playing through so many master games.
This might disappoint you but the only thing you can do in the beginning when learning coordinates is to count, since you will lack the intuition necessary to identify coordinates immediately. As you gain chess experience the intuition necessary to quickly determine the coordinates of a square will be built up to the point where you know exactly where (for instance) f6 is on the chessboard without having to think about it.
But in the beginning (as with anything else) you will have to spend some mental effort to locate squares on the chessboard by their coordinates. To make the learning process quicker you could try to incorporate identifying the coordinates of squares while playing (for instance by keeping a scoresheet of the games you play) but other than that there isn't really a quick method to just learn this without effort.