FIDE Rule 8.1 states:
"In the course of play each player is required to record his own moves and those of his opponent in the correct manner, move after move, as clearly and legibily as possible, in the algebraic notation, on the scoresheet prescribed for the competition.
It is forbidden to write the moves in advance, unless the player is claiming a draw according to Article 9.2, or 9.3.
A player may reply to his opponent’s move before recording it, if he so wishes. He must record his previous move before making another.
Both players must record the offer of a draw on the scoresheet.
If a player is unable to keep score, an assistant, who must be acceptable to the arbiter, may be provided by the player to write the moves. His clock shall be adjusted by the arbiter in an equitable way."
Taking these one at a time...
1. Legible moves. You must record the moves legibly so that if necessary, the whole game can be reconstructed by reading your scoresheet. For a number of years now, it is required that recording is made in algebraic (not descriptive) notation. In a tournament, if scoresheets are provided (usually duplicate or triplicate ones), these must be used if so required by the tournament controller. If you usually like to record moves in your own scorebook, you will have to transcribe the moves to your book after the game has finished.
2. Not writing moves in advance. This rule has been in effect since 2005. This is an important change because some players had become accustomed, even encouraged, to write down their intended move, consider it, then make it on the board. Many chess coaches, including Kevin O'Connell, insisted that juniors did it this way. But note-taking during a game is forbidden, and writing moves in advance could in some circumstances be considered as 'note-taking'. There were also a number of examples where players (usually juniors) would write down their intended move and get their coach or parent to stroll past and give a nod or a shake of the head!
The Rule also states that there are two exceptions. If you want to claim a draw because a three times repetition is about to occur (Rule 9.2) or if 50 moves will have been played without any capture or pawn move (Rule 9.3), then you should write down your intended move that will create the three times repetition or 50 moves, then stop the clock and make the claim. If you touch a piece before writing down the move, then you lose your right to claim on that move. Effectively you would have to wait until a fourth repetition is about to occur, or 51 moves etc.
3. Delaying recording. You are not required to write down your move immediately after you have played it; you can wait until your opponent has replied, and then record both your move and the opponent's move. (You must do this before you make your next move). Several people adopt this method as a time-saving device and I would encourage people to record in this fashion. You can lose several minutes across a whole game by recording your opponent's moves whilst your own clock is running.
4. The draw offer. If, during the game, you offer a draw, you must record that offer on your scoresheet by writing '=' after the move when you made the offer. Similarly, you must record any offers made by your opponent. This is important, because repeated draw offers could be considered as an attempt either to gain time, or to deliberately annoy the opponent. If you feel that your opponent is guilty of this, you can draw the matter to the attention of the arbiter (in a tournament), who will want to inspect your scoresheet to ascertain how often draw claims have been made.
5. Use of substitute recorder. A player who is disabled in some way may be unable to write down the moves, in which case someone else can be appointed to maintain a record of the game. It is common in a tournament for the arbiter to deduct a few minutes, say five, from the disabled player's time, as he will not have to spend any thinking time on recording the moves.
In addition to the above, FIDE Rule 8.4 states:
"If a player has less than five minutes left on his clock at some stage in a period and does not have additional time of 30 seconds or more added with each move, then for the remainder of the period he is not obliged to meet the requirements of Article 8.1. Immediately after one flag has fallen the player must update his scoresheet completely before moving a piece on the chessboard."
In Suffolk League matches, there are two time periods, one ending at the 30-move control and the other at the end of the game. Thus when you have less than five minutes remaining in either period, you can stop recording the moves. However, if this happens in the first time control period, you must update your score after the time control has been reached by doing so in your own time. You may borrow your opponent's scoresheet to do so. If you stop recording in the final time period, then the scoresheet should still be updated when the game has been completed. If both players have stopped recording because they are short of time, then it is acceptable, after the 30th move has been reached, to stop the clocks and reconstruct the game, if necessary by using another board.
Penalties. In an arbiter-controlled tournament, a penalty may be incurred in any instance where these rules have been broken. This can range from a warning, to the loss of the game (or even expulsion from the event!) If your opponent stops recording prematurely, it is best simply to remind them that they should still be recording. Similarly, if your opponent writes down their intended moves before making them, they should be gently reminded that this is not allowed. If they continue to fail to record, or write down their moves before making them, then the clocks should be stopped and the arbiter summoned. The arbiter will normally issue a warning, but can also add two or three minutes to your time if it is felt that you have been inconvenienced.
I've tried to make this as accurate as possible, but if you disagree with something I've written, or have any other thoughts on the above, please comment below.