First, Where are you located and what country did you buy your phone? Some countries have restricted facetime, ie middle east, UAE.
Check if you signed in Facetime with your Apple ID and password (Settings>>Facetime).
Check if you have signed iCloud in.
Check that FaceTime is not disabled in general/restrictions. If that isn't the problem try changing dns servers on your iPad.
Go to Contacts app and select the person you want call then tap Facetime.
Change your address for your currently location. If not works, change it for your native country or for United States (yes, some users have posted in foruns that after change the location to U.S. Everything works at a glance).
If not works, check if the person who you are trying to Facetime has signed in his/her Facetime too.
Most of times the Facetime calls work calling from your friend's email address instead of mobile number. So try to call your friend both ways (his/her mobile number and his/her email address).
If still not working:
1. Go to the Settings App.
2. Tap on Wi-Fi
3. Your chosen network will be ticked. Tap on its white arrow over a blue circle button to its right
4. Tap on DNS
5. Replace the current information with 188.8.131.52,184.108.40.206
6. Try visiting a website with Safari to see if this works
7. Try registering iMessage / FaceTime
If still not working, go to Settings -> General -> Date & Time -> Set Automatically: ON (Yes date time setting has been known to cause issue).
Hope it will be helpful
I am from Guangdong China, my new iPad mini was brought from HK, this is my first time to use iphone product, I have no idea about it. I have already created App ID, but when I was going to activate the facetime,it always suggest me to sign in, i did that, but it always come back to the same picture, maybe you dont understand me,anyway, thanks