In my opinion (John Loughran), the best ways to improve in chess are, in order:
Play lots of games. The more games you play the better you get. If you play against stronger players and lose, you can often use the tricks they used against you when you play someone else.
Write down your moves and those of your opponent. Then after the game play through the moves with them and learn from your and their mistakes, and from their ideas during the game. Sometimes spectators may notice something you both missed. According to strong players this is the best and easiest way to improve. It is like a free chess lesson. One proof of this is that you will often see strong players analysing their games afterwards with their opponents.
It is said that there are more books on chess than on all other sports combined. Books can be divided up into beginners` manuals which cover everything, openings books, middlegame books on strategy, tactics books, endgame manuals, games collections and biographies. Of these the best are beginners` manuals, tactics books and endgame books. Playing through moves on a board helps you remember better than looking at a video or a game on a device, because it is active learning.
Tactics books will show you how to win material using techniques such as forks, pins, skewers, double attacks, discovered attacks, dicovered check, mating threats and many more. They can be puzzle books with solutions at the end. You will find many web sites that allow you to do tactics problems for free. Just Google "Chess tactics". Try puzzles in newspapers when you see them. See Links above too, especially chesskid.com, lichess.org and chess.com.
A friend of mine says that the three most important things you need to practice to improve in chess are: tactics, tactics and tactics!
Apart from learning basic mates, studying endings teaches you how to use the pieces to their full potential, when the position is less complex than in the middle game. It is very useful to know when an extra pawn can be a win or a draw with best play. Lessons learned in endings can be applied to all stages of play.
While studying openings is down at the bottom of my list, the better you get, the more important it becomes. Learn a few openings as white and how to reply to 1.e4 and 1.d4 as black. Some study is worthwhile. Of major importance are opening principles which I summarise here. When my opponent ignores these principles I know that I am winning.
1. Develop your minor pieces: Bring knights and bishops out to squares where they attack some square in your opponent`s camp. Examples of good opening moves after 1.e4 are Nf3, Bc4, Bb5, Be2.
2. Control the centre: Either put a pawn or two in the centre with 1.e4 or 1.d4 and 2.c4 for example, or control it from the wings with g3 and Bg2 or b3 and Bb2 at early stages of the game. Control of the centre allows you to put your pieces there later and create problems for the enemy pieces.
3. Castle early: Get your king safe and your rook active in one easy move.
4. Bring rooks to the centre files: To attack the enemy king who has not castled, or the enemy queen.
5. Develop your queen last when everything has been prepared for her majesty.
6. Push pawns: Push your pawns forward in the centre or on the side where you have not castled. This gains space for your pieces while restraining the enemy pieces, making life difficult for them. If you are better developed then swap pawns off to open the position up to your advantage.
7. Keep your king safe. Avoid moving pawns in front of your king in general as this weakens his defence and allows your opponent a target to attack. If you have castled kingside then keep a knight on f3 handy for defence.
8. Avoid weakening moves. Try to avoid moves like h4 or a4 to get your rooks out to h3 or a3. In general these are bad moves as the rook can often be taken by a bishop (worth less than a rook usually). Do not play your knights to h3 or a3 if you have a choice, as they have only 2 squares to go to from there. A knight on the rim is dim! Better moves are Nf3 or Nc3. Do not play your bishops to d3 or e3 if they block pawns behind them as this blocks the development of the other bishop.
The Golden rule in chess is "There are no golden rules". In other words depending on what your opponent plays and the situation, you may have to break one of the guidelines above to survive. Above all, think for yourself! If you study one or two openings you will quickly see most of the "rules" above usually obeyed and only broken when the position calls for it.
If you have time you can analyse your game afterwards using a computer program or app such as Stockfish, Fritz, Houdini or other software (see Links). Often the program will find things you and your opponent missed. You can also use these programs to practice your openings interactively or try out ideas you did not try out during the game. For practice it is best to analyse first with your opponent or on your own before using an engine.
See Links for lots of good websites to learn from. Many offer a fun and easy way to do tactics problems. I reccommend in particular: lichess.org, chess.com and chesskid.com (even for adults). There are lots of resources available even to free members of these sites. On chess.com look at the Puzzles menu, Learn menu and Puzzles > Drills menu which provides a great way to practice your endgame skills once you have learned them. In the Learn > Lessons search bar if you search for "Play like Beth Harmon" you will find a great lesson asking you to predict moves she made in the series. Fun, instructive and interactive.
If anyone else would like to contribute to this page please do. Send me an e-mail with what works for you, how you improved, your favourite books or resources or any tips you have especially for beginners. Thanks.