Adding on to this. Pressing and holding on your screen usually requires you to have an empty "space" in your home screen - usually a slot minimally large enough to hold an app icon, but if your entire home screen is populated by applications/widgets then your phone won't register the action - it'll instead interact with the widget or app there.
Use pinch-to-zoom on any portion of the display to bring up a menu, then follow Tallman's instructions above by adding a new home screen. I've included a graphic I found online about pinch to zoom in case you're confused.
