If the reset suggested above doesn't work, look at these suggestions for more possible solutions.
1. If you lost sounds for keyboard clicks, games or other apps, email notifications and other notifications, system sounds may have been muted.
System sounds can be muted and controlled two different ways. The screen lock rotation can be controlled in the same manner as well.
Settings>General>Use Side Switch to: Mute System sounds. If this option is selected, the switch on the side of the iPad above the volume rocker will mute system sounds.
If you choose Lock Screen Rotation, then the switch locks the screen. If the screen is locked, you will see a lock icon in the upper right corner next to the battery indicator gauge.
If you have the side switch set to lock screen rotation then the system sound control is in the control center if you are running iOS 7. Swipe up from the bottom of the screen to get to control center . Tap on the bell icon and system sounds will return.
If you are running iOS 5 or iOS 6, the system sound control is in the task bar at the bottom. Double tap the home button and swipe all the way to the right in the task bar to get to the speaker icon on the left side. Tap on that and the sounds will return.
If you have the side switch set to mute system sounds, then the screen lock can be accessed in the same manner as described above.
This support article from Apple explains how the side switch works.
2. Try resetting all settings. Settings>General>Reset>Reset all settings. No data will be lost but you will have to enter all of the device settings again.
3. If you still have no sound, try cleaning the dock connector opening of the iPad with a soft brush and just a little bit of rubbing alcohol.