I suppose I could always export the main templates -- but there's nothing special there, just colour changes, one or two extra graphics, some smilies carried over from UBB, etc. It wouldn't be in a form usable by someone else, and templates aren't necessarily transferable between vB versions -- plus there are code changes to this forum additional to what's in official updates.
If you mean the stuff at the top and sides, though (i.e. integration with the rest of a site) I can tell you how to achieve that pretty easily. Add a hook to global_start under Plugins & Products, which will let you add PHP code to draw in the header/footer code you're already using for the rest of your pages.
$tfa_headinclude = ob_get_contents();
$tfa_bodyinclude = ob_get_contents();
$tfa_footinclude = ob_get_contents();
Under vB you can't easily replace the entire page (<html> tag downwards) so you need to inject stuff between the <head></head> tags, after the start of <body> and just before </body>. What the above does is get that stuff into variables you can use in your template.
The message indicator at the top left just pulls data straight out of the forum tables based on cookied data. Very basic SQL and PHP.
If that went completely over your head, apologies, but if so you'd be better off paying someone to set up and maintain your forum. Or starting with a plain install and learning some PHP afterwards.
Some other TF sites use http://www.vbadvanced.com/
to integrate their forum/site more closely, and also as a content management system.
We're only just now coming to looking at CMS options, as I have very little free time these days.