"How to improve your Marth" by: Dreadlord Santa
God, I wrote an entire ****ing book earlier, but the smashboards server and my computer crashed at the EXACT SAME TIME. It was the most ridiculous thing I've ever seen. I'll try to rewrite it, but I might miss some things.
Regarding your general playstyle, you've got a long way to go before you become a respectable player (no offense) The first thing: You should almost always save your second jump for when you're close to the platform. Use your side+b swipes first thing in your recovery. Saving your jump makes it harder to predict whether you're going to go for a sweetspot or land on the platform directly. You always seem to approach in the air - this is usually a bad idea, since you're safer on the ground. What really confuses me is that, once you actually get close enough to your opponent to hit them, you just ftilt or fsmash him away!
You really should try to learn some aerial combos, rather than getting all your damage from edgeguarding, when you have the opportunity. You used bthrow a couple of times - most people prefer dthrow, since it has less lag and more horizontal send. You got hit with a fair at 100% and just fell to your death without even trying to recover. ALWAYS try to recover, even if it seems hopeless. You never know when your opponent is going to try to get fancy and kill themselves, or just save you from dieing by a flubbed edgeguard attempt.
Everyone else's advice is applicable, pretty much; I personally like shffl'd nairs as a defensive technique against certain characters - Ganondorf, mostly, since he's easily comboed by nairs for some reason. Also, wavedashing is not really better than rolling - they're two separate moves and should be used in separate situations, don't let anyone tell you otherwise. You definitely need to dash around and stuff more often. I can't explain how to do this, really; you'll have to find out for yourself through experience.
Marth's B moves are really situational, and I wouldn't suggest a newbie to go throwing them out a lot. Blade Dance isn't good as a knockback move for Marth, because you can DI out of the good hits. Shield Breaker can sometimes be used at the end of fair chains when they DI up to avoid getting spiked. Dolphin Slash can be used as a surprise KO when they're over 100% and don't get combo'd very well. Counter is a very strange move, someone should write a guide on it's correct usage - I personally never even touch the move anymore.
USE MORE FAIR! I can't really stress that enough. Marth's fair is in my, and certainly a few others' opinions, his best move. I can't really explain how to use it, but watch some pro videos and you should understand. Combos, in general, are absolutely necessary for high-level play. Doing combo damage is much safer and easier than faultless edgeguarding, except maybe against Ganondorf and Captain Falcon. I saw you use an usmash once when the Sheik was above you - I don't know if this was an accident or not, but utilt pretty much always works better than an usmash, since it's better for combos and doesn't have such a crappy non-sweetspot.
Edgeguarding seems to be a weakness for you. Especially against Sheik, you need to try to edgehog your opponent more often. It's an incredibly powerful move after landing a tipper fsmash, since a lot of the time your opponent will just be too far out to recover onto the platform. Against Sheik it's the core of your edgeguarding game, because Sheik has lots of invulnerability on her recovery, especially after the pop. If you don't grab the edge, you're basically inviting her back onto the platform...
I'll try clarify the issue of Marth's grab game. The up chain-throw Marth has can be used on Fox and Falco, up to about 40%, where you can generally do utilt->uair->Fsmash, which ends up putting them at 70-80% and well off the side to the point where Falco can rarely recover. Aside from this chainthrow, though, Marth has few guaranteed hits he can land after a throw if your opponent DIs correctly. Fthrow->Fsmash works on floaties at low to mid %s, if they don't DI away from you. You can also regrab any character after a Fthrow at something like 1-5%, because it will send them low enough so they'll land on their feet. I *think* this works regardless of DI, but don't hold me to it. Also, you can uthrow->utilt most floaties at low %s, and fast-fallers at middle %s.
That should be enough for now. Emblem Lord has lots of great guides on how to improve your Marth game; you should check them out. Any other questions, toss me a PM.