At any time during a guest chat that comes over a queue, you can email the chat transcript to any email address you'd like. Chats between operators and conference rooms are considered private and their transcripts cannot be emailed. How you do this depends on the client you use for chatting.
Operators using an external client such as Pidgin should click on the "chat management link" that displays at the top of each chat and begins, "For transfers, etc...". That link takes you to a page that looks something like this: