Once you have deployed a Linux machine, you will need to log into the Google console and use SSH protocol to log into the Linux server from the VM Instances page.
Connect to Linux instance via Google Cloud Console
Log into the Google Cloud Console and navigate to Computer Engine> VM Instances and locate your new VM.
Click on the "SSH" button under the Connect section. Google will launch a new window with an SSH connection to the linux VM. It automatically logs you in as an admin with an account created with your google username. For example, if your google account is Jsmith@gmail.com, the linux account would be Jsmith@servername.
With this you now have full command line access to linux.
In order to allow external access to the server please see the following article by Google: https://cloud.google.com/compute/docs/instances/connecting-advanced#thirdpartytools
If you get access denied, you may also need to run sudo or sudo su before the command, the account Google creates for you should have sudo permissions.