The base VMs that come with GCE probably do not have any X client software installed - so you would have to install the missing packages.
To connect remotely you want to use a tunnelled ssh connection. There are instructions on how to set up a command line ssh session in the documentation.
All that being said, I would not recommend installing a GUI. You can do everything via the command line, and in the long run it is better to learn to use the command line.