To use live chat as a team you can, for example, set up groups or departments. Using this feature, the users can choose which department they want to talk to. This article talks in detail about how you can set up departments with each provider.
If you've already started chatting with a visitor and come to realize that a colleague of yours can better assist this particular visitor, you can simply transfer him or her to your colleague.
If your live chat tool has its own chat console you can make the transfer through the interface with a few mouse-clicks. If it's running in an instant messenger you'll need to use a keyboard shortcut.