When you step into a set with another player, pretend you have a couple of commentators in your head as you play. Use these commentators to do play-by-play analysis as you play your matches. The reason why this is important is because if you're constantly taking a back seat to your matches, you will begin to notice certain small details that will make you a better player overall.
When you get hit by an fsmash, ask yourself why you got hit by that fsmash and ask yourself how you can keep it from happening again. When you take somebody's stock, ask yourself how you took that stock and how you can do that again. When you lost a match, ask yourself why you lost, what your opponent did right, and how you can throw a wrench in between the cogs of his well-oiled playstyle to stop him from 2-0'ing you.
A big part of Project M is knowing what options exist and knowing how to deal with said options. For example, when you play a Mewtwo, and you see that he is teleporting all over the place, find out when he prefers to teleport. Most Mewtwo's prefer to teleport from the ledge to auto-cancel on stage for a "Free" recovery, but what they don't know is that it isn't that free. Teleporting from ledge usually has a set distance, and if you know this distance, you can stand in a sweet spot near the ledge where you can grab his teleport or chase him if he rolls. (And if you have disjoint, you can even punish his regular get up) As you can see here, I have analyzed when a Mewtwo prefers to teleport and mapped out a decent (But not flawless) punish. As I said before, it's all about knowing those options and finding a way to beat them.
If you think you don't have the capability to hit this mindset yet, just play friendlies with a bunch of people. When you think you're ready, begin engaging in this mindset. You'll notice that as you play more and more friendlies, you will slowly learn all the options that each character possesses as well as how to beat these options.