So with this new forum, we have this thing called "Text Format" below the body field when posting a topic or reply to a forum.
The text format is used to either allow you to use BBCode or a WYSIWYG editor. Until tonight, these were separate items. With the addition of the "Quote" button (w00t!) we've added functionality that merges the two together.
So you can either use the toolbar icons, which will show you what your post looks like as you type it.
OR
You can use BBCode without selecting BBCode in the Text Format. Given this, you may never need to use the BBCode text format again.
The system doesn't much care which version you use, but both will work and you can even mix them. (The reason for this is because the quote button will use BBCode to place the quote into a "Filtered HTML" box. Go figure.)
As always, you can use the quote icon in the toolbar to quote some text, but it won't automatically include another person's name. :)
So have at it. We may continue to tweak how the quotes appear as time goes on, but that's a definite bonus.
--Joel