There are many different ways to write chess moves. The most popular method (described below) is called algebraic notation:

The main idea is that every square has a name like this:

It looks very complicated but it's not! Each square on a chessboard has a first name (a letter) and a last name (a number). The letter identifies a file (column) and the number identifies a rank (row). Now, the important part is to know how to identify the pieces you are moving. You just need to use a single capital letter:

Note that "P" is not used. Chess players have agreed that a move without a letter — such as e4 — is
understood to be a pawn move. You are almost ready to start using chess notation. Just pay attention to the following symbols:

x = Take or Capture

0-0 = K-side castle

0-0-0 = Q-side castle

+ = check

# = checkmate

! = good move

? = bad move

?? = blunder

It’s a great idea to note your games. You can analyze and learn from your mistakes. We all make a lot of mistakes when we are learning a new thing. Don’t worry! Mistakes will help you improve your chess skills. Let’s put in practice what you are learning. We will use the famous "Scholar Mate," also called the four–move checkmate.

(I have used the "p" to indicate a pawn moving, in practice, the "p" is not needed )

#	White	Black		#	White	Black
1	e4			6
2				7
3				8
4				9
5				10

1.e4

#	White	Black		#	White	Black
1	e4	e5		6
2				7
3				8
4				9
5				10

1 e4 ....e5

#	White	Black		#	White	Black
1	e4	e5		6
2	Bc4			7
3				8
4				9
5				10

1 e4 ....e5
2.Bc4 (Bishop to square c4)

#	White	Black		#	White	Black
1	e4	e5		6
2	Bc4	h6		7
3				8
4				9
5				10

1 e4 ....e5
2Bc4....h6

#	White	Black		#	White	Black
1	e4	e5		6
2	Bc4	h6		7
3	Qh5			8
4				9
5				10

1 e4 ....e5
2Bc4....h6
3.Qh5

#	White	Black		#	White	Black
1	e4	e5		6
2	Bc4	h6		7
3	Qh5	a5??		8
4				9
5				10

1 e4 ....e5
2Bc4....h6
3Qh5....a5?? (?? means blunder)

#	White	Black		#	White	Black
1	e4	e5		6
2	Bc4	h6		7
3	Qh5	a5??		8
4	Qxf7#			9
5				10

1 e4 ....e5
2Bc4....h6
3Qh5....a5?? (?? means blunder)
4.Qxf7# (x means capture)(# means checkmate)

The main idea is that every square has TWO names:

one from WHITEs view, one from BLACKs view

BLACKs VIEW WHITEs VIEW

#	White	Black		#	White	Black
1	KP k4			6
2				7
3				8
4				9
5				10

1.KP k4

#	White	Black		#	White	Black
1	KP k4	KP k4		6
2				7
3				8
4				9
5				10

1 KP k4 ....KP k4

#	White	Black		#	White	Black
1	KP k4	KP k4		6
2	KB QB4			7
3				8
4				9
5				10

1 KP k4 ....KP k4
2.KB qb4 (kings bishop )

#	White	Black		#	White	Black
1	KP k4	KP k4		6
2	KP qb4	KRP kr3		7
3				8
4				9
5				10

1 KP k4 ....KP k4
2. KB qb4....KRP kr3

#	White	Black		#	White	Black
1	KP k4	KP k4		6
2	KB qb4	KRP kr3		7
3	Q kr5			8
4				9
5				10

1 KP k4 ....KP k4
2.KB qb4....KRP kr3
3.Q kr5

#	White	Black		#	White	Black
1	KP k4	KP k4		6
2	KB qb4	KRP kr3		7
3	Q kr5	QRP qr4 ??		8
4				9
5				10

1 KP k4 ....KP k4
2.KB qb4....KRP kr3
3.Q kr5....QRP qr4?? (?? means blunder)

#	White	Black		#	White	Black
1	KP k4	KP k4		6
2	KB qb4	KRP kr3		7
3	Q kr5	QRP qr4??		8
4	Qxkb7 #			9
5				10

1 KP k4 ....KP k4
2.KB qb4....KRP kr3
3. Q kr5....QRP qr4?? (?? means blunder)
4.Q xkb7 # (x means capture)(# means checkmate)

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How to Read and Write

International Chess Notation

The main idea is that every square has a number like this:

#	White	Black		#	White	Black
1	52-54			6
2				7
3				8
4				9
5				10

1.52-54

#	White	Black		#	White	Black
1	52-54	57-55		6
2				7
3				8
4				9
5				10

1 52-54 ....57-55

#	White	Black		#	White	Black
1	52-54	52-54		6
2	61-34			7
3				8
4				9
5				10

1 52-54 ....57-55
2.61-34 (Bishop to square 34)

#	White	Black		#	White	Black
1	52-54	57-55		6
2	61-34	87-86		7
3				8
4				9
5				10

1 52-54 ....57-55
2.61-34....87-86

#	White	Black		#	White	Black
1	52-54	57-55		6
2	61-34	87-86		7
3	41-85			8
4				9
5				10

1 52-54 ....57-55
2.61-34....87-86
3.41-85

#	White	Black		#	White	Black
1	52-54	57-55		6
2	61-34	87-86		7
3	41-85	17-15??		8
4				9
5				10

1 52-54 ....57-55
2.61-34....87-86
3.41-85....17-15?? (?? means blunder)

#	White	Black		#	White	Black
1	52-54	57-55		6
2	61-34	87-86		7
3	41-85	17-15??		8
4	85x67#			9
5				10

1 52-54 ....57-55
2.61-34....87-86
3.41.85....17-15?? (?? means blunder)
4.85x87# (x means capture)(# means checkmate)

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(thanks to VINCE KLEMM NM for proofreading my work)