I found these tips here: http://forums.shoryuken.com/showthread.php?t=168866
Not everyone can pull off a Dragon punch easily. Apparently, Capcom put in something (since Street Fighter III) which should ease the burden of learning for new players.
To execute a dragon punch, the instructions say you have to press these:
Forward, Down, Down-Forward + Any Punch Button
There is also a shortcut for executing the dragon punch:
Down-Forward, Down-Forward + Any Punch Button
This should help for players who are really having trouble executing Forward, Down, Down-forward on their controllers. The trick isn't limited just to the Dragon Punch; any other moves which use the same directions as the Dragon Punch can also benefit from the shortcut.
Also, this trick works even for moves which require pushing the directions in reverse. For instance:
Back, Down, Down-Back + Punch/Kick button can be executed as Down-Back, Down-Back + Punch/Kick button.
There are also other shortcuts. For example, to execute the spinning pile-driver, you don't have to turn the stick 360 degrees like in previous versions of Street Fighter. You only have to turn it 225 degrees. For example:
forward, forward-down, down, down-back, back, back-up + punch is enough to execute a spinning pile-driver. You don't have to press UP on the stick or roll all the way back to Forward.
Another shortcut: for moves that are half-circle, you don't have to press all the directions. For instance, if a move is:
Forward, Forward down, down, down back, back + punch
You can execute it quicker by:
Forward, forward down, down, down back + punch
These shortcuts also help you stay on the defensive even while executing your moves.
There should be more tips for new Street Fighter IV players on http://www.shoryuken.com