Session sharing has always been there is not unique to Internet Explorer 8. New tabs, Ctrl-N in any browser (IE5,6,7 FF1,2,3 OP6,7,8,9,10 etc) shares the session data of the global process. It just received a fancy name because now tabs can have multiple processes on the computer (not new either), but will still "share" the sessions. And thats' kinda "new".
It is good that you're aware of this, but it's not so good if you're trying to take this "experience" or "feature" away from the user. If you want that, I'd check into JScript/JavaScript solutions instead and issue a warning when a user tries to open several sessions, but I doubt you'd get a good "prohibit sharing sessions across windows" solution. Even notable banks have already given up on this (they never liked this session sharing thing)
From a design perspective: on the server side, it is rather simple. Just always assume that the session is changed. This can, for instance, mean that on one screen, the user is not logged in, on another he is. That's ok. If he refreshes or goes to another page, you'll show him the correct view: logged in user for the same page.
Just make sure that you check for invalidated data as the result of a changed session in another window (i.e., request). But that's a general advice: be liberal in what you accept, but make sure you validate any input.
EDIT: On extra sessions: just treat them like that. It has always been possible that users open up more then one session for the same user (two different browsers). Just as it has always been possible to change a session through another tab, window etc of the same browser.
On the "solving" side: Configure the session as cookieless. This places the session in the URL query params. Any old window not having the SESSIONID in the URL will not be considered part of the session. However, a warning is in place: this approach eventually causes more trouble then it solves (i.e., now you have to worry about with and without session requests from same user, same browser, same ip and it's still possible to "copy" a session by copying the URL or tab).