Intro: Sup guys, I'm going to get straight into it. We all want to learn how to be a better doctor mario player right? First we have to look at what his general strengths and weaknesses are. Doc is primarily a PUNISHING character. He does not do well being aggressive and taking charge. He excels at capitalizing on mistakes. But depending on your opponent to make a mistake is ********, so you must learn how to FORCE a mistake out of your opponent, or put him into situations where his options are extremely limited and you can take full advantage of that. Doc's GREATEST strength is edgeguarding. Even though I suck and don't generally get kills sub 100%, gimps and edgeguards are what will propel you forward in the metagame. Doc is actually pretty good at getting his opponent offstage once he gets a couple hits in. Work on your edgeguarding for each and every character. I can't stress this enough, it's what I think is honestly holding me back so learn it early!
Comboing: This is EXTREMELY important. Learn EVERY LAST percentage and what your hits do to characters when they're at those percentages. What do you all notice about top level play? A few solid hits generally lead into a kill right? That's because each top level player knows exactly how to follow up whatever hit they land, this is a must. Melee is such a ******** skillful game that dropping a single combo can potentially lose you the match and in turn the set. Learn how to combo (almost) every character out of your grab, and learn what you should do to respond to their DI as well.
Reading your opponent: As I stated earlier, Doc is a punishing character. When you get a read, you must capitalize and punish as hard as possible. Granted, there are some situations where even if you read the opponent, our character limitations prevent us from punishing. Now in the beginning I said Doc isn't a very aggressive character which is true, but it is very rewarding to approach your opponent early in the match/set and see how they respond to your approach. If you shield->wavedash->jab and they shield after the jab, take note of that and attempt to start jab-> grabbing etc. Probe your opponent for responses to what you do in order to read them and turn what they thought was the right choice, into a mistake, and punish FULL FORCE. This is just general game knowledge I know, not so much specific to Doc but if you're a better player in general then you'll be a better Doc player!
Just the intro and some general good player knowledge. Character specifics will be more detailed and such.