Graham Arthur wrote:
when I open an application such as iTunes

Unfortunately, there is no consistent way. It really depends on the specific application you are in. You can try to click the green button with the plus sign in it, but Apple does not implement this consistently in its user interface. In some Apple apps it makes the window fit the content, and in other Apple apps it fills the screen. If it doesn't fill the screen you have to drag the corner to fill the screen manually, or in some apps you can click the green button while pressing a modifier key that's changed over the versions of OS X. Not intuitive.
You asked about iTunes. Unfortunately again, iTunes is the least consistent out of all the Apple apps. The green button turns the window into a mini player. No other application hijacks the green button for this, that I know of. Apple fixed this recently to make it more consistent, but misguided Mac fans caused Apple to switch the green button back to the wrong behavior. This means that in iTunes, if you want the window to fill the screen, you actually have to hold down the Option key while clicking the green button. A little inconvenient and ridiculous, but that's the way it goes with the green button.