The Import
The proper upgrade route is as follows:
1. Download UBB.Threads 7.x (full install file) AND the UBB.Classic 6.7.x importer and extract them to your hard disk.
2. Install UBB.Threads 7.x in a NEW directory (UBB.Threads7 is a completely different product than UBB.Classic 6.7, thus, it is not a simple "update new files and run through the control panel" upgrade).
3. Go through the new install procedure (yourforums.tld/forums/install/install.php) until you reach the "create admin user" screen.
4. Run the UBB.Classic 6.7 to UBB.Threads 7.0 importer.
5. Import Complete.

Re-Using your old location
As UBB.Classic is a perl script, and UBB.Threads is a PHP script, you cannot run UBB.Threads from the CGI-bin (on most hosts anyway). You can however run it from the "Non-CGI" directory, which will be covered below.

If you want to re-use your old directory, simply delete (or rename) your old forum (Non-CGI) directory, and then rename the directory which houses UBB.Threads 7.x; any updates to paths will need to be made to the config.inc.php file in the UBB.Threads7 includes directory.

Redirecting to the new software
Now, if you want to redirect all requests from the old directory, do the following:
1. Open the redirector files which came with the importer and edit the line that points to your install directory and set the url accordingly.
2. Upload the files to your OLD install directory.

It should be perfectly safe to upload these files into your UBB.Threads7 install directory (if you opted to use the old install directory in section 2) as UBB.Threads7 does not use these file names.

Conclusion
Now any requests that go to your old forum location/files should be redirected to your UBB7 install.