I have setup gitlab on my server. I have a successful build of my project using gitlab_ci.
How can I test the result of my build in the browser/How to use gitlab to test and deploy my project?
If I understand correctly, you are using GitLab + GitLab CI to deploy a website.
If that is the case, you must use GitLab CI to do the deployment for you.
Deployment is a very wide subject with many methods and there is not much specific about gitlab to it: if you want to auto deploy just run the test suite on GitLab CI, and then run any deployment command if the tests pass.
One possible method is to deploy with Git as described at: Auto deployment with gitlab
For static websites, one good possibility would be: http://feedback.gitlab.com/forums/176466-general/suggestions/5599145-preview-render-static-html-pages-pushed-to-repos if it ever gets implemented.
In short: first learn how to deploy websites in without GitLab in a way that works for you, then just add the deployment commands to gitlab CI.