To create a new GOG account using your existing Facebook account, hover your cursor over the SIGN IN button on https://www.gog.com/ and click on CREATE ACCOUNT. Then select CONTINUE WITH FACEBOOK.
A Facebook login window will pop up. Enter your Facebook email address and password, and select "Sign in". You will have to confirm that you want to grant GOG.com access to your Facebook profile. You can specify what data will be shared with GOG using the "Edit" option. Afterwards, select "Continue as XYZ", where XYZ is the first name given in your Facebook profile.
A GOG Sign Up form will appear, where you will be required to pick a GOG username (by default it is based on your Facebook name, but with regional characters replaced by underscores).
Next, please enter the email address you want to use with your GOG account, and select CONTINUE TO GOG.COM. A new GOG account, already connected to your Facebook account, will be created under the username you picked.