I feel as though melee fundamentals should be categorized in terms of, muscle and mental fundamentals. The question of "how do I improve?" is such a an uninformed question and begs for a universal answer. I believe that the answer to that question is largely relative to the player (in the later stages of progress), but not so much in the beginning. It is not enough to say that you want to be good at melee, to become good at melee. You have to actively problem solve and chase after your goal. I believe that the first step taken on any journey of improvement should be made to establish ones own character. "What is my end goal?" and "How much time am I willing to devote to my goal?" are two broad questions of self-evaluation that I think are worth asking yourself as soon as you become invested into the game.
It isn’t silly to want to be the best, for it's only an unrealistic goal it you are unwilling to undertake the hardships necessary to reach the upper echelon of play, and are unwilling to learn what these different hardships may be. But before you are prepared to learn you must hold yourself accountable for your own performance.
Those looking to improve should never make excuses for their own failures, rather when defeated you should devote time to understanding why you were defeated. It is not the games fault. And, it's not your character or your opponent’s play style that is holding you back, it’s your own mentality and lack of proper practice (which directly correlates to a lack of ability and skill). It is okay to lose, because when you lose your many weaknesses are being exposed. It is your duty to identify and correct these weaknesses as necessary.
Being good at Melee means many things. It means actively problem solving in and outside of matches. It means being technically sound, having in depth game knowledge regarding character on character punishment, and understanding how to win neutral. Being good at melee also requires solid mentality which can be called a positive growth mindset. (And much more)
To preface discussion on positive growth, we must be able to differentiate between negative and positive patterns in improvement. Negative hurdles for growth separate the player from the game, while positive tools help to further immerse the player into it. This means that something even as simple as having a conversation during a match only serves to negatively impact your play as it takes away from you concentration on the game itself.
I'm just jotting my thoughts down, will continue doing so later.