This is basically a list of resources I did not have time to include in a more appealing manner. Many of these resources are extremely useful, though you are still able to find success in Super Smash Bros. by just playing without these resources.
Playing Smash - Improvement - Information - Resources - Competitive - Discussion
A guide to netplay for Melee, which allows you to play Melee online with other people, or offline, on a computer. Note that you will need an adapter (such as this one), and that you will need a fairly powerful computer.
Smash Ladder, an online matchmaking system for netplay.
The Nintendo Wii Console.
A guide to hacking your Wii to play Gamecube isos. (Please only do this if you are not able to find a physical copy of Melee, or it does not read discs properly. We are not responsible if you damage your Wii or get DMCA'd for pirating.)
A Gamecube Controller. Note that Japan imported white non-Smash logo Gamecube controllers are of the best quality (aside from modded ones, which are in a grey area regarding tournament legality), but any will do. For best results, get any first-party Gamecube Controller.
A guide on practicing.
A list of attacks and techs, accompanied with descriptions.
A youtube playlist of the advanced techs of every character, as well as general techs (February 2017). Note that the list is not fully exhaustive, but has more than enough information. It can also help in choosing a character to main.
SSBM Tutorials, a youtube channel full of videos on improving and techniques to implement.
SmashWiki, a wiki with various information about the game. Note that some information may be incorrect or outdated.
Handbook for Melee, an android app with various information and frame data about Melee.
I Knee Data, a website with various information on melee.
I Knee Data's calculator, a web app that can calculate the knockback and trajectories of every move with every condition you can think of.
The /r/Smashbros wiki, filled with various information about the game, links to discussions, and competitive information.
The /r/SSBM wiki, which is the above, but more focused on Melee.
The 20XX Melee Training Hack Pack, a mod that can help solo practice (or even regular practice). Note that this mod is generally not legal at tournaments. Also, v3.02 may be of more use than v4.05 in some cases.
20XX TE, another mod that is meant for streamlining tournament setups, but can also be used for practice. A key feature is the replay feature, which can allow you to analyze your own gameplay to fix your mistakes.
The Smash Brothers Documentary Series, a series of videos documenting the competitive history of Melee from its birth to late 2013.
The Smash Liquidpedia, a wiki focusing on competitive Smash.
A guide on attending tournaments.
VGBootCamp's stream, a Twitch stream that focuses on competitive smash content. Note that many other tournament and individual player streams exist as well!
The /r/Smashbros subreddit, which has discussion on gameplays, tournaments, and Smash-related news.
The /r/SSBM subreddit, which is more focused on Melee and gameplay.
SmashBoards, a forum with discussion and various resources and information.
Smashcords, a list of Smash-related discord servers.