There are a few core aspects of your game that are applicable to any character and people are always learning about, even professionals. Things like movement, edgeguarding, neutral game, punishes, combo game, recovering, tech chasing, and your defensive game. You could improve these specifically by a few methods:
For movement, you want to go into training and train a bunch. The fundamentals of movement are things like wavedashes, wavelands, wavelands from ledge, shinedashes if you play a spacie, dashdancing(maximum distance for your character).
Edgeguarding practice: If you play a character like Marth, know every option you have. Know when to neutral b instead of charging a forward smash. Know when to down tilt. Know when to go for a simple edgehog. Know when a simple edgehod isn't enough and you go for a dair back onto the stage. This applies for all characters, and against all characters. For example, edgeguarding against a Samus is quite a deal different from edgeguarding a Fox. (Samus you can often wait on the stage, or drop down to kill while she's tethering. Fox has the option to go high, which Samus usually doesn't, and Fox has phantasm and firefox to contend with).
Neutral game: One of the hardest things to 'train,' as it is often learned through hours of playing better people and being punished for every mistake you make. Tech skill comes into play here a lot. For example, your Falco is immensely more powerful in the neutral game if you can shinedash, shine -> waveland on platforms, or spam lasers effectively using isai drops on platforms. Otherwise just play, and play a lot.
Punishes: Kinda relates to the combo game, but specifically you need to be able to recognize an opponents' errors and capitalize on them. When a Samus accidentally up b's out of shield and doesn't hit you, she's entirely helpless in the air. You need to know what move is best to begin the punish, and how to make sure it ends in a kill.
Combo game: Watch combo videos, and practice against people who DI well. Always can improve here.
Recovering: Know EVERY option, both for getting to the stage, the ledge, and from the stage to the ledge. This gets more complicated with characters like Samus(my main if you hadn't guessed), who have many options off the stage. How many bombs do you lay? Will they drop down and try to kill you in tether, and if so which way do you airdodge to mix it up and throw them off? When you get to the ledge, do you wavedash on, or come up with an aerial? Or stall for a bit? All these are important. You learn them by playing good players who know how to edgeguard, and being punished endlessly for poor recovery. Every time you are killed recovering, think if there was a better option you could've done there that would've saved you, and apply this next time.
Tech chasing: Know your dashdance, and the cues of other characters to be able to tech, etc. If they miss a tech, punish it accordingly. Learn your options and when to use them, and then develop your mindgames and you can go for risky reads on rolls/etc.
Defensive game: Ties into neutral game, movement, and punishes as well. Evasion is a part of this, and there actually is a way to train this. Fight a level 9 CPU and try to avoid it for as long as possible. Also punish it when it attacks your shield, or misses an attack. Also learn your DI! Make it a reflex to survival DI. When being comboed, try going to platforms or the edge, and see which works best. Know your enemy and DI in the hardest way possible to avoid them continuing the combo.
In general some ways to get better:
Fight CPUs and tech chase them to death. Then play a human. Its much harder, but you need to start somewhere. Do NOT get into bad habits!
Go into training and practice movement to death. Especially with characters like Fox, you need to have extreme tech skill to move around quickly
When you play people and lose, KNOW WHAT YOU DID WRONG. Next time, don't do it. And just like that, you're getting better!
