I was a competitive chess player in my youth and am currently ~2300 on Lichess. Here are key aspects of any training regimen:
* Tactics - I did thousands of tactics puzzles using a program called CT-ART while under a time limit. I would have to complete 25 puzzles within 5 minutes while making 0 mistakes. If I made a mistake I would have to start from the beginning.
* Core positional concepts - Understanding pawn structure (double pawns, isolated pawns, passed pawns, pawn majorities, etc.), control of central squares, open files, king safety, and so on.
* Endgames - Many players neglect endgames. Master the basics: common rook-and-pawn and pawn-only endgames, how to checkmate with 2 bishops and bishop + knight, etc. Read Silman's Complete Endgame Course, Basic Chess Endings, and Dvoretsky's Endgame Manual (for advanced players) to improve your endgame play.
* Openings - Many people have mentioned learning openings, but it is generally a mistake for beginners and intermediate players to focus on this aspect of their game. It is not especially useful for a ~1000-rated OTB player to learn 15+ moves of theory in the King's Indian Defense only to end up in a position where there are slightly better according to theory but have no understanding of their position. It is better to center your opening repertoire around easy-to-learn openings and focus on improving other aspects of your game until you are strong enough to handle positions outside of opening theory.
* Tactics - I did thousands of tactics puzzles using a program called CT-ART while under a time limit. I would have to complete 25 puzzles within 5 minutes while making 0 mistakes. If I made a mistake I would have to start from the beginning.
* Core positional concepts - Understanding pawn structure (double pawns, isolated pawns, passed pawns, pawn majorities, etc.), control of central squares, open files, king safety, and so on.
* Endgames - Many players neglect endgames. Master the basics: common rook-and-pawn and pawn-only endgames, how to checkmate with 2 bishops and bishop + knight, etc. Read Silman's Complete Endgame Course, Basic Chess Endings, and Dvoretsky's Endgame Manual (for advanced players) to improve your endgame play.
* Openings - Many people have mentioned learning openings, but it is generally a mistake for beginners and intermediate players to focus on this aspect of their game. It is not especially useful for a ~1000-rated OTB player to learn 15+ moves of theory in the King's Indian Defense only to end up in a position where there are slightly better according to theory but have no understanding of their position. It is better to center your opening repertoire around easy-to-learn openings and focus on improving other aspects of your game until you are strong enough to handle positions outside of opening theory.