Lesson 3: Half-circle special moves. (Away, away-down, down, down-towards, towards + button) Again, like above, try to do the same thing, only start out holding away instead of down. Try it fairly quickly, and try not to make common mistakes like jumping (done more often this way than just a quarter circle.) Street Fighter takes a lot of practice, and learning these special moves isn't exactly the easiest thing in the world. Keep trying, and I'm sure that you'll know how to do these in no time.
Lesson 4: Full-circle special moves. (360 spin on controller + button) To be honest with you, I even find a hard time dealing with this special move. I usually jump first and then spin the joystick around, but can never do it on a normal controler. I even tend to take a hit on purpose so I don't move in order to spin the controller around 360 so I can do the special move. Even though these moves are the most devastating when they connect, I still think it would be fair if Capcom were to make these into 180 moves. After all, the characters that have these to begin with are a bunch of slow-pokes anyway that car hardly get in contact with the people. To tell you the truth, and I know I'll get hate mail back on this one, but I think that it's not even worth trying to practice these guys in the beginning. Wait until you're really good at the game before you try learning these brutes. And when you do start, try practicing at first with a turbo controller. Hold the turbo button down that is needed, and spin the joystick around while jumping at an opponent. That is the easiest way I can explain it, but remember when you get to the arcade, they don't have turbo there. Then it is all based on timing, if you want to waste your money on these guys to begin with.
Lesson 5: Dragon punch (Towards, down, down-towards + button) This is the deadliest of all moves generally. When you master using this special move, you have pretty much mastered using all of the fundamental moves. If you get scared off learning the 360, don't worry about it for now. When attempting this move for the first time, try to walk forward first and then try to do a fireball. Pressing forward quickly and trying to do the fireball almost always works when you have mastered the fireball. There are even times when I play that I end up doing this on accident when I'm trying to set up my opponent for a combo or trying to fake them out. Even in a blocking position to start out with, and then getting up to walk forward will cause you to do this if you don't hesitate sometimes before doing a fireball. Again, practice practice practice.
Extended lessons: Efficient charging/repetitive dragon punch/fireball, etc.
Lesson 1: Rotation moves (Fireball, dragonpunch sequence). Once you have mastered doing the special moves, you should then master being repetitive with them. The easiest of these is the rotation special moves. All you need to do is keep doing it over and over again for maximum effectiveness. The easiest way I can explain this is if you can get into a fireball fight with Ryu or Sagat (they tend to throw them out constantly) and win! then you are considered a master at this. By winning, I mean that you can defeat them with only fireballs. It's tough. But you can do it with practice. Do it on an easy level though. Next, you should try doing the repetitive uppercut. Test it vs. Ken. He tends to do these all of the time. The best way to test yourself is to first do fierce uppercuts, and do one as soon as you land. This means leaving NO ROOM for anything else. Consistently do them, no pause. You can consider yourself a master when you can do them repetitively with a weak punch. You will know you are doing them consistently, because they will never be able to finish saying "Shoryuken." They'll get to "Sho" or "Shoryu" and that's about it.
Lesson 2: Various charges. With those characters that have charging specials, there are a lot of ways to be efficient when you are charging. First of all, as soon as you do a special move, immediately hold back/down again to continue the charge. As soon as the fireball hits/you land on the ground, you should be able to do one again immediately. The only exceptions to this is possibly a fierce punch sonic boom type that doesn't allow a lot of time (but if you get good, you should only need maybe a split-second more), a weak flash kick (although these can be done as well repetitively when timed precisely, but allow a slight split second for a charge anyway), or if the opponent was close when you did the move (sonic boom for example). This should not have an effect on down to up charges though, as you can still charge in the air. The same goes with away to towards charges (as long as you are in the air). Charging in the air should come naturally. It is a blocking position anyway, and should be done nearly at all times. Finally, you can also be charging while blocking moves or being hit. Just because you took damage or are blocking doesn't mean your time is reset. If anything, it will give you MORE time to charge, and can counterattack more easily. Generally though when counterattacking this way, you want to use a weak button. It will put you back on your feet quicker or will go slow enough to catch the person off guard.