I just realized I had a lot of typos so I might as well post it here with some fixes...
- Learn how to wavedash on command - This is extremely important as a mewtwo player; it is absolutely essential to wavedash, and wavedash perfectly. If you you can do it, good. If you can do it every single time you command it, great. If not, practice and do so.
- Shadow Balls are you're friend - A lot of mewtwo's I see spam the crap out of the uncharged shadowball. That's ok.. but don't over do it. Throw them out there when you know you're safe from where you are, becuse if you do it too close, there will be enough lag time for the opponent to punish you. If you get a fully charged shadow ball, don't waste it. You really really have to use it wisely. The harder it is for your opponent to read it, the better. Also another really good advanced tactic (which mostly works against fast fallers like cfalc, fox, and falco) is jump toward them and hit your analog stick the opposite direction of your jump once you're in the ai,r and start charging your shadow ball. A lot of people underestimate this move. They can't run up and grab you and it's difficult for them to attack you, although lookout for spaced smashes. When they get caught up in it you can do two things. #1 you can stop charging immediately and turn around and grab them real fast as they fall from the air, or #2 you can let it keep charging and hope they DI in front of you, that way when they finally get out, you can unleashed a nearly or fully charged shadow ball. Watch germ's mewtwo vid on youtube.com against Zele's cfalc if you don't get what I mean.
- Mewtwo's dtilt is arguably his best move - In my opinion it is. The reason why it is soooo great is because it's fast (fast enough where it's difficult for the other person to shield grab it), it's good range, it by-passes their shield a little bit, and most importantly IT SETS UP FOR COMBO'S. Now most normal falling speed characters you'll be able to hit them 2-3 times in a row, after that go in for the grab or Fair. Slow falling character usually 2 hits then jump up with a fair, and fast fallers... oh boy, you can do a lot to them... you can hit them anywhere from 3-6 times in a row with a dtilt and end it with a grab, Fair, or even a down smash if they're at the right percentage (this actually works pretty decently against fox).
Grab - Mewtwo's grabs are obviously one of his best arsenals. But what do you do once you grab them? First I highly recommend getting as many hits with A as you can. A little trick I use when playing people is I listen to their controller. If I hear them twirling their control stick like crazy then I'll throw them much faster.. if I don't then I just keep on pressing A... Now some for some other chars this is kinda bad to do because it gives the other player time to prepare for the DI, but with mewtwo, his grabs are so slow anyways, most of the time they'll see which way they're being throw before you actually throw them and DI appropriately. A lot of people think since mewtwo'sup throw or back throw is the strongest so they always do those ones. But don't forget about the down throw! Down throw is great if you can do this: TECH CHASE. Observe peoples behaviors, learn to do it. Now if you're playing on a big stage like FD, then a lot of hte time the opponent can DI away and then tech away and they will be unreachable... but they don't do it always... If they don't then you can dashdance back and forth and grab them where ever they happen to tech to. If they decide not to DI out of it, then the beauty is your can grab most characters again! So back to the earliery problem, what if they DI and tech away from you? Well after they do it after a while you'll begin to realize they're going to do it everytime. So what I find useful to do after that is jump forward and shadow ball then immediatley wavedash to dtilt them right as they get back up. Now what if you're on a small stage like Yoshi Story... oh boy let the fun begin!! Since the stage is so small, they're limited to how far they can DI and tech away, which therefor enables you to reach them and grab them again! So basically what that means is if you tech chase perfectly, you can get them everytime! So when is it good to back throw or up throw? When they're high enough percent and can't be effectively down thrown. Remember, the faster faller the character, the harder it is to kill them with an up throw, especially if they DI. So if you're fighting fox, I recommend to try to get him off the stage and keep him from getting back, but if you're fighting like Samus or peach, UP throw for the kill. Another thing I forgot to mention is if you're playing on a big stage like FD, it's usually best not to down throw and tech chase. You're much better off throwing your opponents up and getting them with an uair on their way down. Mewtwo's uair has HUGE vertical range and good priority -- most characters can't match it in priority or range when coming down. Last thing about grabbing, remember to ALWAYS jump cancel throw while running. To do this simply press Z and Y (or X) at the same time. It makes you're grab slightly farther and you won't have to worry about stopping short (which for some reason mewtwo sometimes does when you dash grab).
Arials - Mewtwo has good arials. You already heard me talk about the uair. It's also worth noting that it's a good finisher for combo's, especially when your fair isn't in range. Fair is another one of Mewtwo's best moves. It's quick and really powerful. It's also a great finisher and it's also easy to hit fast fallers with it multiple times in a row. The Nair is one of Mewtwo's best moves as well. A lot of people think since it usually hits people that are coming with an attack that it has good priority. But it doesn't. The reason why it does so well intercepting attacks it because it's soooo quick, quick enough to stop the opponent's attack animation BEFORE it can hurt you. Learn to spam this move like crazy. It does good damage, it throws people off, and it breaks a lot of combos. It even leaves you invulnurable for a little bit against a lot of projectiles. But ALWAYS REMEMBER, this move does not have good priority, so if you jump into some who has range on you and they're charging a powerful attack like a smash... (ex. fox's upsmash) you're done... The Bair is also very useful, but use it carefully! I almost only use it for people that are recovering. It works extrememly well against a lot of people who recover, especially (fox, peach, mario's, falco, cfalc, ganon, and so forth). Pretty much almost everyone. But like MookieRah has said before, beware because this move does open you up for attack, but of course you don't really have to worry about that when jumping out there and preventing them from getting back . Finally you have the Dair. Of course you probably already know that this is a spike, and a rather decent spike I must add. The beauty of it is it's hard to see and identify the actual animation. I recommend using this move sparingly. I find it works best in cases where an opponent was barely knocked off the edge (not too far) and is quickly trying to get back, forgetting to sweet spot. This is especially good against cfalc and ganondorf -- they are perfect targets for the spike, however, the Bair is almost always better.
A nice little glitch - Mewtwo has a cool trick where he can pull opponents through the stage on battlefield. This is down back hanging the ledge, pressing back, then forward B really fast. Now a lot of character CAN recover from this ESPECIALLY IF THEY PREDICT IT! But still there are even some that are screwed no matter what. The most important thing to realize with this move is to do so that you're opponent never sees it coming. Like if you for no reason jump back and grab the edge and just wait there, then of course someone's gonna see it coming from a mile away. Don't do it. A better method is to do it totally out of nowhere, for example if you were knocked off the edge and they're trying to edge guard but miss and you grab the edge. Right then and there they're thinking you're are going to somehow try and get back on stage.. but that's when you hit them with it out of the blue! I also find it best to teleport the ledge immediately after I do it and edge hog if appropriate.
Approaches/How to get in - There are a lot of different way to get inside with Mewtwo. The two most common ones I can think of are these. #1 shoot a shadow ball and hope it distracts them by either hitting them or them putting up a shield and then run or wavedash in with an attack or grab. This is ok but the next one is better. #2 Wavedash in with a dtilt. Seriously it doesn't get any better than this. This approach is almost flawless. You can even combine #1 and #2 also : shadow ball, wavedash to dtilt. And of course the dtilt combos into almost anything you want. Another approach is the jump to backwards charging a shadowball like I explained earlier, but use it cautiously. And finally you can go in with Nair. But I really really discourage doing this too much. Because if you do it too much and it precomes predictable, your opponent will match it with a smash to the face. Using an Nair when you're already in is pretty good though.
Down Smash - Lots of people seriously overestimate this move but the more and more I use it the more I realize how good it is. Although it's pretty slow, it does have some conciderable knock back. The best part about it is its HUGE encompassing hit box. I use this move mostly to edgeguard. If you watch Taj's vids you'll see that he uses it a lot too. Don't be afraid to charge this over the ledge or a little bit back from it while they're coming back, because they might just over shoot their 3rd or second jump and miss the sweet spot, then bam!! People mess up... Capitalize on it. And if you miss... it's not that big of a deal, because they can't really punish you for it. A side note: vs. Fox and Falco, I'm pretty sure they can't get past a down smash by forward B to the edge, because there is a slight delay in between when they get there and when they actually grab the ledge and get their invincibility frames.
Mewtwo's Recovering is one of THE best recovering's in the game - The only person that can even compete with mewtwo's recovery is Jiggly. Jiggly probably does have THE best... but hey, second best isn't bad. Not only is it crazy far, but it's also very versitile and hard for opponents to hit you while recovering (if done right). I recommend doing 1 of 2 things. Either you can come in as high as you can float far enough into stage so that they can't reach you (and if they try and predict and follow you below then teleport away from them in the oppostie direction of what you're traveling), OR teleport sweet spot the ledge. Sweet spot works wonders.. I'm telling you.. learn to do it and do it well. Also learn the trick where you can get extra height off your second jump by doing an arial sometime during the second jump (Fair, Bair, and Uair work good). It should lift you up higher if you do it right. It's saved my butt countless times. This crazy recovering also enables you to going FAR out from the stage in order to prevent a person from recovering.
Learn to Double Jump Cancel - This is when you attack immediately after you're second jump, stopping you short in the air completely. This will allow you to do many combos much better.
Mewtwo is a Combo bag - The reason why mewtwo is bottom tier is simple, he's is freakin HUGE, and people can combo him like none other. One of the best advices I've gotten was from Bob$ who got his advice from Isai, and that is: Don't get hit. Now I'm sure you're thinking well no sh*t. But seriously think about it, if you don't get hit, you don't lose. It's that simple. So play it safe, know when to go in, when not to. Know what moves you can match and which ones you can. Play smart. I don't care how good you are with your fingers, you're only going to get so far without being able to play smart. And even though Mewtwo is a major Combo bag, HE can combo many characters like non other as well, especially FAST FALLERS!!
Shield Grab and Jump out of your shield like crazy - Since mewtwo is arguable the worst character in the game, you almost HAVE to rely on other people making mistakes. Some people may argue with me but I believe this to be true. So if someone isn't spacing and gets to close with an attack, shield grab them. If they're just out of grab range, jump out of your shield with a Nair or Fair. Punish them!
One last trick I've discovered recently - Ok this is pretty sweet. It works well most characters except slow fallers, but suppose you're opponent is backed up against the edge and you grab him. What do you think is the best thing to do? I'll tell you: down throw. Why? Because it puts them exactly where you want them to be. Note: this works best starting around 30 - 40 percent. After you down throw them, they will be recluctant to DI away from you off the stage. It's just something that they're naturally trained not to do, and for good reason! But this is the nice thing about it, if they chose not to DI off the stage and toward you or not at all, you are able to simply grab them again in midair. Do it again, they'll most like do it again, and again. Finally they'll say, ok screw this, I don't want to keep on getting chain thrown, so they'll DI off the stage breaking the chain throw. Sounds like a good plan for them... wrong! This is exactly what you WANT them to do. You are basically giving them no choice but to do this, and so that's when you charge the down smash and release it as they try to frantically get back to the stage! If they try coming back really low... then just turn around and grab the ledge! It's freakin beautiful!! Try it! This works best on FD, because on other stages they might be able to bounce high enough so they land on the platform above you... but it's still work a shot.
. Hopefully I can get some vids up one of these days... 
