Here are the instructions for setting up a new TM1 server (sometimes also known as a TM1 model). This can also be used for taking a copied TM1 model and setting it up on a new physical server.  The steps are:

1. Copy the tm1s.cfg file from an existing model
2. Change the ServerName, PortNumber, LoggingDirectory, and DatabaseDirectory within the copied tm1s.cfg to the name and location of the new server (model).
3. Create a new server instance in Cognos Configuration and edit the location to point to the folder where the copied tm1.cfg is located.
4. Start the server instance
5. Open TM1 and login to your model