After watching the Smash documentary last summer, I immediately began my quest into becoming a competitive Melee player. With my 401st placing out of 1000+ at Apex 2015, my first national, I thought it was time for people to learn my training regime from my beginnings.
First off, you need to choose a main. I had originally chosen Marth because I was so entrigued by Ken and Mew2King in the documentary and who doesn't like Japanese RPG swordsmen? Try exploring each character's moveset, speed, and weight. At this point, I would really suggest choosing one of the S tiers rather than a character you like. They have much more potential than the others even though they are matchups everyone knows. Not to say that A and B tiers aren't good (because I still get rekt by them), but you will find yourself acheiving more at lower levels with S tiers.
Once you have a character chosen, learn these techniques in order:
All of those techniques can be practiced alone. Be sure to also use these techniques during friendlies in order to build your muscle memory in times of pressure. Don't worry if you are losing a lot while using advanced techniques. You will eventually learn how to properly use them in matches.
I didn't include it on the list, but I think one of the most valuable things to practice is movement. Just simple wavelanding onto platforms and dash dancing with wavedashes in between helped me out the most in my game. Being able to outmanuever and juke out your opponents works well as you're flustering them with your speed.
Be sure to pratice on legal stages only!
Next, we have techniques that are better practiced against real opponents:
All of these techniques have unique frame data and inputs that can be seen on Smash Lounge. For me, I haven't taken much consideration into looking into frame data and it's working out fine, but I do believe there's a Mew2King-eque point in which I should learn about it.
These techniques also require a long amount of time to learn them. When I first started last July, it took me a week to get both L cancelling and dash dancing down, then later on it took me a month to get ledge teching and so forth. Times may vary from person to person, but don't fret. You will eventually get it down.
Super Smash Bros. Melee, the most perfect game ever created
In addition to all of those universal techniques, there are character specific techniques such as waveshining, Ken combo, Shino stalling, etc. There is a set of videos called "Trials" that feature most character techs for Sheik, Fox, Falco, and Marth.
Along with videos, I began learning my Marth from watching old videos of Ken during his King of Smash era and then eventually transitioned to players like The Moon, Mew2King, PewPewU, and Tai.
For the most part, time spent = skill gained. Throughout the whole month of January, my prep for Apex included 3-5 hour practice sessions late at night. During that period of intense training and for a couple of weeks after, I felt my gameplay was at its best. Sadly, since school caught up, I've lost a bit of tech skill, but I've compensated by playing smarter. With this time spent, entering smaller tournaments and playing friendlies benefits the most. Both help out finding out other player's styles, which allow for you to adapt to them during the match. Also, the more tournaments you play in, the less nervous you'll become over time.
Along with these videos and such, the 20XX Hack Pack is a great way to practice alone. It allows you to practice more techniques alone than the vanilla version. You can practice spacing aerials so you don't get shield grabbed, power shielding Falco lasers, and more. You can find the updated version on Smashboards.
The main thing is to have fun during this whole experience. Of course your competitive side might make you angry and frustrated if you keep losing or you can't waveshine properly, but you'll eventually get it. Always remember to play with the intent to learn and display your knowledge of your character against another. I'm not a professional player (maybe semi-pro?), but this is what helped me start to get to my current skill level and it'll be still rising just as everyone else is, even the top players.