How can you log in to an instance using the serial console if I cannot add a public IP?
Can i just copy and past the public key value into my computer to use putty or other ssh client to login into he instance?
From what I have found you need to generate a new SSH key (using putty or ssh-keygen) – CHANGE THE USERNAME@HOSTNAME at the end of the key to just the username you use for gcp. From there you will need to add the public key you generated to the SSH Keys section of your vm.
Go to vm instances in the google cloud console, click the instance you want, click edit then scroll down to the ssh keys section. Add it there and click save.
You should be able to ssh into the vm now with the command ssh