To enable the screen rotation feature, do the following.
1. Swipe UP from the bottom of the display to reveal the Control Center.
2. The last icon at the top is the screen rotation lock feature. If the icon is highlighted, then rotating to landscape mode will NOT occur.
3. If the icon is highlighted, tap on it. Now you should be turn your device sideways and get the screen to do so as well.
NOTE: This will not occur with apps or games that are designed for portrait mode only.