Captain Falcon, huh? My friend mains Falcon, so I can help with that.
I'll start with the bad stuff. The matchup for us is... Unfavorable, to say the least. Falcon is just too fast to handle. As much as you would like to punish a whiffed dash grab with a smash, you can't. Falcon almost always has time to shield or roll away, so for punishes, you need to rely on grabs and reading his defensive options.
Obviously Zard is a master of being comboed, and the Cap is no stranger to taking advantage of that. When you're inevitably being thrown around, don't try to airdodge out, as it only leads to Falcon hitting you with a more dangerous move. Wait until he's out of jumps and forced to land and fastfall back to the ground, where you can more easily deal with him. Ultimately, if you just let him throw out some nairs and uairs, he gets some damage off; he can only kill you if you set yourself up for it.
Now, the knee is something you have to look out for. I'm not sure how obvious it is to people who aren't familiar with the matchup, but I immediately know when a Falcon is about to knee. This is the part where you tell him no. Rock smash that ****. Even a sweet spotted knee is nothing to rock smash. He puts himself in the perfect position to take the full 30%, and now he's above you. (Or dead, depending on his position and damage.) Even better, use rock hurl for this matchup. Frame one super armor and aerial coverage is a pretty good exception to the "let yourself get comboed" rule.
Flamethrower is a great tool in this matchup. (And every other matchup.) If you need to take a breather, just hit B. This is one of the only times when you have a natural advantage over Falcon. He can't run through it, and running at you is basically the only option he has. He will jump now. Falcon mains aren't patient people. As soon as he leaves the ground, release B and select the punish of greatest effectiveness. If you think he'll hit you before you have a chance to do anything, just shieldgrab. Uptilt, rock hurl, and even fly will work otherwise. Our frame six upsmash will do the trick best.
Flamethrower is, as we all know, great for edgeguarding too. This is especially true for Falcon. Angling this down over the edge can cause KOs if Falcon doesn't mash upB. The only problem there is that flamethrower runs out. The optimal place to stand is right where flamethrower doesn't go over the ledge, but rather hits the stage and goes horizontal, so falcon has to snap to the ledge. Now, all of his getup options are impossible, save for rolling. That's very easily punished with a smash or even fly.
In terms of sideB options, you should use dragon rush. (Although it's hilarious when you predict an approach and Falcon runs right into a blast burn.) We all know dragon rush's benefits, so I won't go over those, but backthrow into dragon rush (is that a true combo at 0% on Falcon? Can someone confirm or deconfirm that?) is great for carrying falcon offstage, and you can even use a bair and still recover. You don't really want to go offstage besides that, however. (Unless you're a cool kid and like going for spikes.) Falcon's offstage options are just too good for a character like Charizard to handle.
Other than that, just use a lot of SH nairs, jabs, and dtilts. Your goal is to stop Falcon from getting up in your grill. I don't know how the exact matchup ratio is decided, so if someone more experienced could figure that out, that would be cool.
EDIT for 1.0.8: It's important to note that Captain Falcon is a fastfaller, and you may need to get him to higher percents than normal to dthrow combo him. He will most likely try to fastfall and/or airdodge to the ground, so don't just follow up with aerials, mix it up with grabs or smash attacks.