Maximize Screen

Just bought a new 12" iBook and am using a Mac for the first time. When I open Safari or other apps the window does not use the entire screen. Is there a quick way to maximize the window to use the entire screen? The green button doesn't quite get there.

Just click and drag the corner of the window to fill the screen. It will save this setting so when you quit Safari, it will open at that same size the next time.
The green button is not a Maximize button, it only fits the window to the "best" dimensions for the contents of the window.

If you mean it doesn't use the entire screen because there's a bit to either around the dock that isn't used then, the only way you can do so is if you turn dock hiding on. I sometimes do this if I need the little bit extra space at the bottom.

For my 12" I turn dock hiding on and leave it on, the little extra space it provides is really worth it considering its still just as functional.