Here is a solution from iMore.com.
iMessage and FaceTime are wonderful, empowering, enabling technologies that... can frustrate the crap out of you at times. One of those times is when you update or restore your iPhone, iPod touch, or iPad to a new operating system - like millions of people just did with iOS 7 - and it stops working. If you're having trouble with iMessage or FaceTime, if they won't activate or simply won't work, here are some things you can try:
Turn FaceTime or iMessage off and then back on in Settings.
Launch Settings by tapping the icon on the Home screen
Scroll down to Messages or FaceTime
Toggle the switch from on (green) to off (white)
Wait a minute
Toggle the switch back to on (green)
Wait for it to re-activate
Hard reboot your iPhone, iPod touch, or iPad
Make sure you're on Wi-Fi
Hold down both the Home button on the front, and the Sleep/Wake button on the top of your device
Wait for the Apple logo to appear
If it still doesn't work, repeat step 1 (turning FaceTime or iMessage off and on)
Reset network settings
Launch Settings by tapping on the icon on the Home screen
Tap on General
Scroll all the way to the bottom and tap on Reset
Tap on Reset Network Settings
If it still doesn't work, repeat step 1, then step 2, above (Turning FaceTime or iMessage off and one, rebooting).
One of those, or a combination of both, should get you going again. If it works for you, or if you find any other ways to trouble shoot, let us know in the comments!