TheKmanOfSmash
Smash Ace
Doing well in the neutral game requires a great deal of understanding about your character's options, the options of your opponent's character, how said options interact with each other in the Match Up (spacing, zoning, punish game, etc), and knowing the habits and tendencies of your opponent, as well as noticing your own habits and adapting accordingly.
Knowing characters' options and how they interact in the MU can be learned by looking at frame data and/or watching gameplay videos where different players use specific moves and trying to understand why they worked (people may have MU analyses in the character forums if you have trouble figuring it out yourself). And these things can be practiced in training mode and friendlies. But adapting to the habits of not only your opponent but yourself as well is probably the most challenging part and is something that you can't develop overnight. It requires you to actively think about every decision you do and it requires you to have confidence in your decision making and confidence in yourself, generally. I can't really teach this well, but I can link you to a very good guide that can teach you a lot about noticing player's habits and what to do about them.
You have to make an account on the website to view the guide, but I really think it's worth making the account. When I had started competitive Smash as a Brawl player, this guide opened my eyes to exactly how I'm supposed to get better at playing Smash and helped pave the way for my improvement and how I'm supposed to keep on improving.
http://ssbfc.com/discussion--guide-learning-to-mindgame-t-22784.html
It's oriented towards Brawl, but the same concepts applying to not only Melee and P:M, but to nearly all fighting games.
I hope that helps somewhat. Sorry if my answer is too broad. I can't really give a precise and specific answer to your question.
