GitLab One-Click App runs atop of Ubuntu 16.04.
You should be able to access it via Console. If you don’t see anything in Console Window or you thing it bugged out, try to press any key on your keyboard.
Also you would not be able to login right after creation if you used SSH key on creation (in that case you was not mailed root password, and you can’t login without resetting it).

You would have better experience if you use SSH instead of Web Console.
How To Connect To Your Droplet with SSH will explain you how to do it on Windows or Linux/OS X.

If you need help setting up GitLab One-Click App, you can refer to How To Use the GitLab One-Click Install Image to Manage Git Repositories.

If you want to learn more about Ubuntu and firsts step on it, Initial Server Setup with Ubuntu 16.04 could be helpful (just make sure if you decide to follow it and you want to enable firewall, enable ports needed for GitLab too).