Lets start with some terms so we are all talking the same "Language"
The Messages App in Mountain Lion can do two sorts of Text chats
1) iMessages to iOS devices and other Macs using Messages (that have registered an Apple ID for IMessages)
2) Instant Messages (IMs) to various services such as AIM, Jabber or Yahoo (In iChat 6 or later)
iChat will Text chat to a person using an Google Talk ID if they are logged in to a web Browser > Google Mail or iGoogle) with Talk Enabled on their Account
You just have to have a Jabber account of some sort logged in on iChat and have added them as a Buddy.
They could also be using any one of a number of Instant Message Apps that allow either PC or Mac users to login to multiple services.
Google have also released a Stand alone App called GoogleTalk for PC users.
It may be simpler if you don't want to set up Messages for a Jabber ID that you use your Web Browser and A Google Mail Login having Enabled Talk on your Account.
To be clear.
iMessages are a form of communication
They are text Messages to iOS devices or Macs who have registered an Apple ID for iMessages
They can not be sent to any old email Address
They cannot be particularly, sent to other services such as AIM or Jabber (this is despite the Messages window having the Text chat area)
Google run a Jabber server using the IDs of the Google Mail Service with the "Talk" option enabled to be valid Jabber IDs
You needs to use a Jabber ID of some sort in Messages (Or iChat)
In the Mountain Lion Community here at Apple Support Communities there is a "Messages" Category tag you can use when posting there.
Some of the regular Posters filter the larger forums (Communities) using these filters.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously