There are various ways to deploy stuff. Gitlab is simply a version control system with a web frontend. It stores the application’s source code and its entire history, but it’s not a deploy framework.
If your application does not need to be compiled, you can simply clone the repository onto the target machine with “git clone”, and then you can install it the same way as if you were installing it from an unpacked tarball. To update to the latest version, you simply git pull in the application folder, update the settings if necessary, and restart your application.
If your application requires compilation, you’ll need to set up a build server (unless you fancy doing manual monkey work) that generates either a compiled version that can be dropped into place, or an installer/package/… - how to do this is beyond the scope of your question however.
Your best bet? Simply talk to your developers. They built the thing, so they should be able to provide you with installation instructions.