Chatting with AIM buddies is only available in Gmail.
Before you can chat with someone using a Google Chat property (i.e Gmail, Google+) you'll need to invite them by following the instructions below. Your friend will see the invitation above their chat list asking if they'd like to be able to chat with you. Until they accept, you'll see 'Invited' next to their name in your chat list.
Once they've accepted your invitation, you'll see a status button to the left of their name in your chat list, which indicates whether they're available (green), busy (red), idle (yellow), or offline (gray). At that point, just click on their name to send them a chat message.
To invite someone to chat:
In the search box at the top of the Chat area, type your friend's username. If they're already in your Contacts, Gmail will pre-populate their username.
Google+ Users: If you invite someone to chat who isn't a Google+ member yet, they won't receive an invitation to join Google+. (You can invite them to join Google+ from the Find people tab, or by choosing to share something with them.) If that person does join Google+ and adds you to their chat list, you'll be able to chat with them.
Megan is a Google Chat expert and the author of this help page. Help her improve this article by leaving feedback below.