Practice combos in training mode and play other players online that are at your level and better than you.
This is the ultimate combination and path towards becoming better. The practice of combos will increase your finger speed, familiarize you with the hitboxes of each character's moves and the subtleties of their movements, and give you an understanding of how to link moves together (SSB64 is THE combo game after all). Playing equal and better players will teach you new ways to use characters, how to move about the stage faster, what kind of mindgames and habits can be used and exploited, and encourage creativity. Playing only opponents FAR better than you is not always useful as being constantly overwhelmed by their superiority in-game does not always give you a chance to learn and try new things.
Even playing inferior opponents is great for when you want to learn to implement a new aspect of your character into your game. As an example, I once spent an entire game using only shine-cancels with Fox against an inferior opponent so I could learn to use them quickly and well.
Combos and real opponents (online or on console) are the best way. You need both to improve the fastest. People pick up combos as they go but watching vids on youtube and copying combos from matches/combo videos and then learning them means you'll have that advantage that much sooner than learning by constant trial and error over hundreds of matches.
Also, for the record: NotFrogles would make a large number of experienced players here today have their ***** handed to them. Don't feel too bad about it.
