If you already have a Facebook account, you can simply sign in or register with Gumtree by clicking Sign in with Facebook.
A window will pop up asking for your Facebook credentials. Once you enter your email address and password for Facebook, this will allow you to sign in to Gumtree with the same account.
Email correspondence will be sent to the email address associated with your Facebook account.
You don't need to set up a password specifically for your Gumtree account if you sign in through Facebook, however a password can be set under Profile Settings or by clicking Forgot Password and following the prompts.
Sign in with Facebook is simply an alternative way to sign in to Gumtree, and it saves you the trouble of remembering multiple passwords and sign in info!