Talk with the carpet dealer. If you're buying new carpet, the carpet dealer should be able to provide you with key information, including the face weight.
Contact the manufacturer of the carpet. The face weight is a common feature of carpet, and the manufacturer should be able to supply you with this figure.
Look at the product description for the carpet. The product description can be found at the store or on the manufacturer's or dealer's website. It should provide you with the face weight.
Compare your carpet with similar carpet if it's already installed in your home and you don't know who installed or manufactured it. Find a carpet that is made of the same material and has a similar thickness and feel. The face weight of this carpet can give you a good estimate for the face weight of your existing carpet.