@jzehner4192 tbh not so hard to find. In the "US Chess Rule Book" it says under 15A. Manner of keeping score.:
"In the course of play each player is required to record the game (both the player’s and the opponent’s moves), move after move, as clearly and legibly as possible, on the scoresheet prescribed for the competition. Algebraic notation is standard, but descriptive or computer notation is permitted. The player must first make the move, and then record it on the scoresheet. The scoresheet shall be visible to the arbiter (tournament directors) and the opponent throughout the game."
However as a comment below:
"[...] TDs are advised to first (and possibly second and third) issue warnings to players that do not comply with this revised rule before enforcing any time penalties [...]."
So in an USCF tournament (and also FIDE ones), you don't have to fear to loose if not following this rule. However, keep in mind that this is an suggestion, a Tournament Director (TD) can basically rule as they wishes.
However, there is the following: 15A. (Variation I) Paper scoresheet variation.:
"The player using a paper scoresheet may first make the move, and then write it on the scoresheet, or vice versa. This variation does not need to be advertised in advance. The scoresheet shall be visible to the arbiter (tournament directors) and the opponent throughout the game."
In addition to:
"TDs may penalize a player that is in violation of 20C, Use of notes prohibited if the player is first writing the move and repeatedly altering that move on their scoresheet before completing a move on the board."
I won't bother searching when the variations kicks in, but the use mentioned in #13 is in both cases strictly forbidden. When behaving OTB, just remember that you're a man/woman/... of culture and thus shall not do anything that causes irritation. This includes, but is not limited to:
Eating smelly food, being loud, being unfriendly, irritating your opponent (and writing down moves and erasing them surely is irritating).
I highly encourage you to be friendly, which includes, but is not limited to:
Giving your opponent at the start of the game a firm handshake (as well as at the end, no matter the result), saying hello in a genuine kind tone and maybe chatting a little bit before the game. When the time of your opponent is running because they didn't hit the clock, you can and shall mention this (in my national federation, it's also encouraged to move after an appropriate amount of waiting time)! Many opponents are also willing to analyze the game with you afterwards - that's a nice experience. As a last tip from me: Your opponent has all the right to play the game. A lot of people get grumpy when the opponent doesn't resign (a childish trait). If it's the last round of the tournament, some opponents (me included) will be in favor of a quick draw. It's up to you, but I don't like the feeling of loosing the last game. If you think so too and your opponent doesn't - refer to the last sentence.
Edit: After posting this, I see that you've also found the paragraph. If you are not familiar with rules (like me in the case of 'when to apply the variation') you are always encouraged to ask the arbiters! They will help you and explain to you all main features like claiming draws (not that easy if never seen before) etc.
@jzehner4192 tbh not so hard to find. In the "US Chess Rule Book" it says under 15A. Manner of keeping score.:
"In the course of play each player is required to record the game (both the player’s and the opponent’s moves), move after move, as clearly and legibly as possible, on the scoresheet prescribed for the competition. Algebraic notation is standard, but descriptive or computer notation is permitted. The player must first make the move, and then record it on the scoresheet. The scoresheet shall be visible to the arbiter (tournament directors) and the opponent throughout the game."
However as a comment below:
"[...] TDs are advised to first (and possibly second and third) issue warnings to players that do not comply with this revised rule before enforcing any time penalties [...]."
So in an USCF tournament (and also FIDE ones), you don't have to fear to loose if not following this rule. However, keep in mind that this is an suggestion, a Tournament Director (TD) can basically rule as they wishes.
However, there is the following: 15A. (Variation I) Paper scoresheet variation.:
"The player using a paper scoresheet may first make the move, and then write it on the scoresheet, or vice versa. This variation does not need to be advertised in advance. The scoresheet shall be visible to the arbiter (tournament directors) and the opponent throughout the game."
In addition to:
"TDs may penalize a player that is in violation of 20C, Use of notes prohibited if the player is first writing the move and repeatedly altering that move on their scoresheet before completing a move on the board."
I won't bother searching when the variations kicks in, but the use mentioned in #13 is in both cases strictly forbidden. When behaving OTB, just remember that you're a man/woman/... of culture and thus shall not do anything that causes irritation. This includes, but is not limited to:
Eating smelly food, being loud, being unfriendly, irritating your opponent (and writing down moves and erasing them surely is irritating).
I highly encourage you to be friendly, which includes, but is not limited to:
Giving your opponent at the start of the game a firm handshake (as well as at the end, no matter the result), saying hello in a genuine kind tone and maybe chatting a little bit before the game. When the time of your opponent is running because they didn't hit the clock, you can and shall mention this (in my national federation, it's also encouraged to move after an appropriate amount of waiting time)! Many opponents are also willing to analyze the game with you afterwards - that's a nice experience. As a last tip from me: Your opponent has all the right to play the game. A lot of people get grumpy when the opponent doesn't resign (a childish trait). If it's the last round of the tournament, some opponents (me included) will be in favor of a quick draw. It's up to you, but I don't like the feeling of loosing the last game. If you think so too and your opponent doesn't - refer to the last sentence.
Edit: After posting this, I see that you've also found the paragraph. If you are not familiar with rules (like me in the case of 'when to apply the variation') you are always encouraged to ask the arbiters! They will help you and explain to you all main features like claiming draws (not that easy if never seen before) etc.