Settings > Message > iMessage and make sure that is on
Settings > Message > iMessage > Send and Receive and make sure that your mobile number, iCloud email address and email address are there
If after doing all this, it still does not work, try a reset,
Reset your iPad by pressing the 'Sleep' and 'Home' button at the same time for about 15 seconds or so. Your iPad will then go through a reset / reboot procedure and will be ready for use within about a minute.
Don't worry about doing this as you will not lose data or settings.
Good luck and do report back.