Do you see a lock icon in the upper right corner of the iPad next to the battery indicator? If you do then you have the screen locked.
Try flipping the switch above the volume control on the side of the iPad. If that does not unlock the screen then try this. Double tap the home button and swipe to the right in the task bar at the bottom of the iPad. Look all the way to the left. If the lock icon is showing there, tap it to unlock the screen.
You can set how you use the side switch in your settings. Go to Settings>General>Use Side Switch to: Lock Rotation or Mute. Whichever feature you choose to use with the setting here, the other feature will be available in the task bar.
So if you use the switch to lock the screen, you have to swipe in the task bar to enable the muting of system sounds.
You can read about the side switch here.
There are some apps that do not allow you to change the screen orientation so that is a possibility if it only happens when you use certain apps.
If none of these things help, try a couple of old standby's ...
Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
Reset the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons.
Rotation lock can be located in two places depending on how you have it configured in Settings/General/Use Side Switch. The easy one is the side switch. But if you have configured the side switch for Mute, then Rotation lock is a bit tricky to find. Press the Home button once to go to the Home screen. Press the Home button twice to lift the Apps Bar/Dock. One finger swipe, left to right to reveal the iPod controls and the rotation lock is the icon in the bottom left corner.