Shut off your fireplace and allow it to cool completely down for a few hours prior to looking for your model number.
Look for the informational placard somewhere on your fireplace's base. This will be a small square containing information like the manufacturer's name, the model number and the unit's serial number. The location of this card will change depending on the unit, so check on the top, sides and even underneath the fireplace, if possible.
Look inside the original documentation that came with your fireplace. This documentation will contain information about how to use the fireplace as well as information about the unit itself, including the model number. This model number should be listed on the cover as well as throughout the book, including on the specifications listing.
Return to the store where you purchased your fireplace, if applicable. If you added a fireplace to your home after purchase, you can return to the store where you originally got the unit and have them look up your purchase records. These records will contain the model number information.