Well, I'm not even near an expert on fighting games but from my experience that "training" mode is there basically for you to memorize your moves and learn how they hit, range, speed and things like that, unless the game have those options to make your opponent act like a normal CPU (I mean make them move and I think that SFIV can do this).
First of all just try to make the basic attacks come naturally for you. You could aim to be able to easily perform Hadoukens (Down, Right, Punch), Shoryukens (Right, Down, Right, Punch) and Tatsumaki Senpukyaku (Down, Back, Kick) as a initial goal. When you are able to naturally make those special attacks you should be ok to do nicely against the CPU.
From there it will all comes down to practice. Learn when it's safe to use a Shoryuken as Misery said, what to use to start a combo, where on the screen will your attacks be able to hit your target and things like that.