Screen Sharing needs an AIM or Jabber Login at both ends.
It cannot be done from the iMessage account on thre Messages end.
Screen Sharing starts in iChat 4 in Leopard.
It needs and Internet speed similar to maintaining a 1-1 video chat.
It is AIM to AIM or Jabber to Jabber.
In iChat 6 Apple added the ability to add Yahoo account to iChat but this does not do Video and therefore cannot do Screen Sharing.
In Messages the iMessages side invokes the FaceTime App to do Video so it als cannot do Screen Sharing.
If your Apple ID ends with @mac.com, @Me.com or @icloud.com then these are also valid AIM Screen Names.
You can add them in Messages as a Separate "AIM" account.
If you have a Google Mail ID then your can enable Talk on your Google account setting at Google and you then have a valid Jabber ID.
Facebook is the same if you enable "Chat".
You can get Jabber IDs from a host of Jabber servers.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
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
"Limit the Logs to the Bits above Binary Images." No, Seriously