If your iPhone screen isn’t rotating, then you are either using an app that doesn’t rotate, or you need to check the settings. Open an image or some other app that you know has rotated in the past and see if they are rotating. If they aren’t, then check the settings. To do this, look for a curved arrow in the top right hand corner of your screen next to the battery meter. If you see that the screen rotation is locked and all you have to do is turn it off.
To turn off the lock on the screen rotation on your iPhone, if you have iOS 7 or higher, swipe up from the bottom of the screen to get to the Control Panel and tap the screen rotation lock icon. If it is set to “on” it will be white and if it is set to “off” it will be black. If you have iOS 6 or earlier, swipe from left to ride to find the Music app and music player controls. The screen rotation app that looks like a curved arrow will show up on the far left and you can tell if the lock is turned on if there is a lock inside the arrow. If that is the case, just tap the icon and the lock will disappear.