Hitting L to throw yourself into the ground to propel yourself forward or backward is not good design. Its not intuitive to learn at all.
Why does it need to be "intuitive to learn?" Learning through intuition is the domain of casual play, for games that want to be a relaxing pastime that players can coast through without having to do things like practice and research. In that world, things need to be intuitive-- or otherwise forced upon you through unskippable "now-you-try-it" tutorials-- because most gamers can't be bothered to read text in the game itself, let alone to look up information discovered by other players on a message board.
The competitive scene is an entirely different world. Even if developers intentionally try to make it otherwise-- as with Brawl-- those who try to coast through will
never succeed. Now, in your case you've already taken the important step of going to a message board to learn. At this point, intuition isn't needed. We can tell you
exactly how to perform a wavedash. We can describe in great detail many of its potential uses, and we can link you to videos of other players utilizing it. If you still won't learn it, it is not because it needs to be more intuitive. All the information is here and readily available; there's nothing left for you to intuit.
I know others have said this, but it bears repeating in this context: In the grand scheme of smash, learning to wavedash is easy. This is not because of other purely technical barriers, but because of barriers that are *not* purely technical, like spacing, recovery, DI, and combos. These are much more difficult to explain or understand because they vary constantly based on the actions of your opponent, whereas wavedashing is always the same sequence of inputs and timing for each character, regardless of who your opponent is or how they are playing. It's is a bit like riding a bike on a flat street. It seems crazy at first, but once you get it down you never have to learn it again. Actually learning to play Melee against competent players, though? That's riding a bike with cliffs on either side, and the ground shifts around beneath you.
Harsh as it may seem, if the flat street is so daunting to you, it's possible you're just not a competitive player and this really isn't your kind of game.