Super Smash Bros. is an intimidating franchise to get into competitively, especially when talking about Melee. Between all the complex mechanics and technical skill involved, it can be hard at first to find your way around the scene and figure out how to level up as a player.
As they have made a habit of doing, the YouTube channel SSBM Tutorials comes in with an excellent guide to help new players level up quick. The pointers revolve around focusing practice around one main character, playing at as many tournaments as possible, and focusing training mode time on your punish game. All of these lessons can be applied to all Smash games, and all fighting games in general for that matter. They go in-depth on each point, explaining why and how to get these things done, so watch the whole video and learn how to set yourself up for success.
Source: SSBM Tutorials (YouTube)