To extend gjmnz's suggestion -
If you click the little green button on the top left and it still doesn't fill the screen, you can always grab the lower right corner of the window with your cursor using your mouse/trackpad, and change the size of the window to as small or large as you like. Pulling it all the way to the right corner of your screen will obviously maximize it. (those angled ridges on the bottom of the "wood panel' mark the area to click on to stretch the window).
Then, if you're planning on using Garageband for awhile and don't want to be distracted by other visual elements, you can banish your dock for the session. You do this by going to the finder, and simultaneously pressing:
option + command + D.
Moving your cursor to the bottom of the screen will make the dock temporarily pop up again, and pressing option + command + D again while in the finder will make it permanently reappear.
When working in Garageband, Logic, or other music software, I too like to open up the window to fill the screen, and get rid of the dock.