Find somebody who's better at competitive Smash than you and keep playing them. You will get beaten, but that's okay, that's how you improve. Every time you get beaten, consider what you did in the match, what mistakes you made, what you did right, and how you can refine it and improve. Every failure is a tiny victory if you discover something to help you get better.
Play different opponents, preferably people who have a wide range of characters that you can get used to. Fighting different character types can help you improve your respective skills: rushdown characters teach you how to dodge and evade, projectile characters teach you how to powershield and (if you have the option) reflect and absorb, etc.
Practice your fundamentals. Know the terminology. Footsies, neutral, advantage, disadvantage, that kind of thing. If you have good fundamentals, then you have half the battle won from the moment you hear the word "GO!"
Dedicate yourself to a character, maybe two or three at most, depending on their matchups and how comfortable you feel with several characters. Know their matchups, their abilities, their best stages, their tech if necessary. Know the character inside-out, feel totally comfortable using the character. Practice every day and try to discover something new every time you play with the character, even if it's just what you're doing wrong or how to use your specials more efficiently.
There's no right or easy way to get better. It's a constant, gradual process, you need to just keep practicing and constantly try to find new things. Even if you don't think you're getting better or you feel absolutely defeated, you will get better just by being aware of your mistakes and getting back up to try again. And, possibly a coy platitude, but I find it's very important nevertheless:
HAVE FUN! :3
