When you press on and hold on an icon, a small screen within a screen should appear. This small screen is the area of that particular screen where icons can be move to.
If all the space on that smaller screen is used up, you can't move any apps around, since there is no place left for them to be moved to.
You will notice however that as you press and hold on an icon, a small trash can will appear on the lower right side of the screen that says Delete. If you drag an icon to that trash can it does not delete the app, it merely deletes that apps shortcut icon. The app itself is still in your apps screen.
So if you need to free up some space on a particular screen, drag one or more icons to the trash can to get rid of them. Once you have arranged the screen you are working on to your satisfaction, you can go back to the App screen. Find the apps whose icon shortcuts you deleted and move them to a new screen.
One of the great things about this phone is the number of ways you can configure it. It's been said there are 221,184 ways to order a Whopper at Burger King. I think that pales in comparison to the number of ways you can configure this phone