Chess notation is truly for your inner chess nerd. It requires a proper setup, and some folks like to have a pen and paper handy. For practice, doodling, jotting down evil chess plans...
First, you can save yourself a lot of trouble if you buy one of those durable, roll-out chess-mats found at some game stores. Get one with the coordinates all labeled for you. I no longer have mine :/
The 8 Rows, or Ranks, are labeled 1 - 8, with 1 being closest to white. The 8 Columns, or Files, are labeled a - h, left to right, from white's perspective. A white square should be at white's h1.
Now for some codes. Every type of piece has its own type of code.
K = King. Q = Queen. R = Rook. B = Bishop. N for kNights (K is taken). Pawns have no letter, only coordinates. The pawn in front of the white queen is the "d2 pawn", in the example photo ->
This pawn moved from d2 to d4. In notation you usually write only "d4" on your notepad.
Each line of your game's record will have a pair of moves, written left-to-right for white & black. The log can read top-down or left-right but be sure to use labels! 1) e4 ... e5. 2) Nc3 ... Nf6. Etc
When you make a move, you list the piece by its letter-code, then write the square it moved to. Re1 means your rook moved to e1. If there were 2 rooks, you might write Ra1e1 to be more specific.
Captures are described with an "x". Rxe2 means your rook captured whatever piece that was on e2. Some notations you'll see in a few books have the identity of the captured piece. RxB, or whatever.
Nxc6 ("kNight takes c6"). Or, NxN, sure...
"Checks" are indicated by including a + after all the other codes. Checkmate is ++
Bxc6+ ("bishop takes c6, check!")
If you "castle king-side", you write 0-0. Queenside is 0-0-0. (castling is a sneaky chess move where you move your king 2 squares to the corner and put your rook at its side. It's a legit defense!
That's the gist of it... Thanks for reading!