Hi,
In Messages in Yosemite and El Capitan you can start a FaceTime Chat (Audio or Video from the Detail option top right of the main Chat window) when you are text (iMessaging) that person.
This is a work around if the other person has Yosemite or El Capitan.
This works fro Screen Sharing as well (You have to enable it in System Preferences > Shairng)
If they have an older Mac and only have Messages 8 in Mavericks, Messages 7 in Mountain Lion or a version of iChat then the only way is (was for the moment) using an AIM to AIM to Jabber to Jabber connection staring from the Buddy list (As opposed to the main Chat window).
This method has issues at the moment caused by the SNATMAP server.
This is a server run by Apple that is supposed to connect Internet based Buddies.
Exactly what the issue is with this server is a mystery.
We know it is working at one level as you can do port tests to the ports it uses. (It no longer responds to Pings but that way lies Attacks and is probably why).
The server will still connect LAN based Audio and Video chats (Bonjour account or two separate AIM Names on two computers on the same network for instance).
There are reports that if the router can be and is removed from the set up then connections seem to work.
This excludes other computers and iPhones and iPads on your LAN and any other internet connected devices such as TV, Apple TVs, X-Boxes, PlayStation and some types of Satellite On Demand connection or even some Cable services so it is not very practical.
In some cases ISPs hard code the Login info into the device so you may not be able to use the computer to Login to the ISP anyway.
At present there can be no progress on this front.
You can report it. http://www.apple.com/feedback/ichat.html
This is the correct page despite the lack or updates.
It does mean some of the info requested in the lower Drop downs has to be entered in the Free Text Area.
There will be no reply.
It sort of work on a pressure system, once it meets a critical mass sort of thing then Apple will sort it.
10:01 p.m. Sunday; October 11, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad