Note: Please don't be intimidated by this post. Please read.
Alright, man *claps*. I watched it all the way through and I thought it was enjoyable. It remind me of when I started getting into competitive Smash. I wasn't that good... okay, I wasn't good at all (I thought I was the best) but I slowly started using more advanced techniques. I saw you attempt to PTP and I notice a few short hop neutral air attacks. Good start.
I'm not going to so much critque you and your friend (I play Dr. Mario AND Falco... and those same colors, too, lol. You have good tastes
) rather than lead you in the direction of teaching yourselves. If I watched the video and critqued everything, you'd have a page long essay on things you might not even understand.
So, for starters, I would recommend looking at this:
http://video.google.com/videoplay?docid=-6268917341431368191
It is the Advanced How To Play Guide. It is a
must if you are looking to get competitive or "insanely good" at this game. It might seem intimidating at first, but trust me, it gets easy. It becomes second nature.
I'd also like to throw this out there before you possibly become discouraged: It does take work to be good, but it might seem overwhelming to you. It's not. Thirty minutes, even less, a day is all you need to get good decently fast. If it seems like you're doing even WORSE than you were before you started trying to get good... that's good. It's natural for that to happen. When you learn something new and start incorporating it into your game, you'll do worse at first, but in the end you'll come out higher than you were before. So start with that guide.
Then, for Dr. Mario, I'd recommend a read through this:
http://smashboards.com/showthread.php?t=55939
It's a textual explanation of the essentials you need to know about Dr. Mario. Smashmac was kind enough to make a video explaining some of the things as well, so if you are going "...What the ****?" that should help you. I'd recommend watching it even if you aren't going wtf. I even read through the Doc guide every now and then myself, just to refresh on some things. I'm a pretty decent player, but it never hurts.
Also, you've come to the right place if you're looking to get good. The people on this board (the Dr. Mario board) are pretty nice people and will be willing to help you, even if it seems like it takes them forever, XD.
So now you understands the basic competitive moves and know how to use Dr. Mario well... what next? Practice, practice, practice. If three practices in a row scares you, I'm sorry. It's just I emphasize it. It isn't much practicing, but if you find you can't do something, I bet twenty minutes of solid practice will iron that out. If you can do something fine in practice, but have trouble doing it in actual gameplay, that's natural. A really common thing is people not knowing the right time to wavedash. It becomes natural to you. Just slowly start to incorporate it into your game. That might cause you to suck more and die at times you normally wouldn't or miss kills you normally would have gotten, but it will help you in the long run.
Smash is full of potentially confusing acronyms and concepts. I won't even begin to go into them, but thankfully AlphaZealot has done that for us:
http://smashboards.com/showthread.php?t=42749
That there is your encylopedia to all terms Smash. It also includes a color-coded picture of which stages are neutral (the ones you have set on random), banned stages, and counter-pick stages if you're interested in competitive smash, such as tournaments, or just want to play serious every now and then with your buddies by doing sets.
If you are interested in tournament play, the character match-up chart would also be a good thing to look at and familarize yourself with. That doesn't mean memorize it, as the match-ups will become obvious to yourself after awhile, probably. Ever notice you have a **** hard time against Marth and that **** sword? Dr. Mario doesn't do so well against Marth, at least compared to other characters. That doesn't mean you can't beat him, but it will be harder. However, some characters will be a punching bag for you, just because you counter them so well. Again, that is mainly only if you are interested in tournament play, but if you want to get really good, you're probably heading in that direction.
I think I've covered enough for you and given you a decently paved path to follow... so much for not giving you a page long essay. Heh, sorry. Good luck on your road to smashing glory. If you have any questions, feel free to ask.
EDIT: Sorry, I thought I should add this as well: I probably wouldn't have gotten as good as I am now without watching videos. By watching more advanced players play, you can see how the character is kind of supposed to be played. Kind of like Cyphus' textual guide put into action, if you will. Combo videos and matches on Youtube are a great start. They really helped me.
So without further ado:
Dr. Mario Video Thread -
http://smashboards.com/showthread.php?t=105097
Here you can find bunches of matches of Doc vs. a wide array of characters. The matches of Bob$ vs. Falcomist would be great for you to watch. Now, these Falco's don't play like your friend does, but the Docs do play how you would normally fight that character (on an advanced level). Give 'em a watch.
Combo Video Thread -
http://smashboards.com/showthread.php?t=84888
Aww, the combo video thread. What a time killer this thread can be and enjoyable at that. Combo videos are a great way for you to start thinking about how you can kick *** and take names. Good Dr. Mario combo videos to watch are Overdose, Take it and Get Out, The Medic Man, and DBR Evolution-Bob Money. Good stuff.
Alright, I hope that got you started. Good Smashing to you.