Do you have to pay for Apple to unlock your phone?

What kind of unlock?

1) iCloud: Activation Lock - http://support.apple.com/kb/PH13695 - This is a security feature so only legitimate (i.e., not stolen) redistribution of devices is possible. See: Turn off Find My iPhone Activation Lock - https://support.apple.com/HT201441 - If an activation lock was put on a device, only the owner of the account that applied the lock can remove it.

2) Device lock: If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled - https://support.apple.com/HT204306

Apple generally does not unlock iPhones.

How is it locked exactly?

What happened?

Did you forget your passcode?

If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled - Apple Support

Is it Activation Locked?

Find My iPhone Activation Lock - Apple Support

No. Go to the top right corner of this page and ask there, There is an opportunity to make direct contact there.