Using FaceTime http://support.apple.com/kb/ht4319
Troubleshooting FaceTime http://support.apple.com/kb/TS3367
The Complete Guide to FaceTime + iMessage: Setup, Use, and Troubleshooting
Troubleshooting FaceTime and iMessage activation
Using FaceTime and iMessage behind a firewall
iOS: About Messages
Set up iMessage
Setting Up Multiple iOS Devices for iMessage and Facetime
FaceTime and iMessage not accepting Apple ID password
Unable to use FaceTime and iMessage with my apple ID
For non-Apple devices, check out the TextFree app https://itunes.apple.com/us/app/text-free-textfree-sms-real/id399355755?mt=8
How to Send SMS from iPad
I have a similar problem. WIFI is fine, iPads and another Mac all can use FaceTime. With the MacBookPro ()S 10.6.8) FaceTime rings at the other end, but cannot complete the connection. The same is true in reverse. FaceTime sees the incomming call, identifies the caller, but then cannot connect. The only new thing in the mix is a HP 5520 printer which I just added to the computer. I loaded and updated the printer software on the MacBook Pro. I did not have to do so on a MacBook Air (OS 10.9.2) as it appeared to already have the printer software.
Skype works fine on the MacBook Pro. I shut down Skype and iChat and restarted the MacBook Pro, but FaceTime still failed to connect to either outgoing or incomming callers.