How do I link an already established local git repository to a new remote repository and push all files to remote?

My scenario is that I have created a local git repository using SourceTree. As I worked on my project I would commit to my local repository. Nothing new there with Git. So I have a well established Git repository now that I would like to put on a remote server and do the normal Git push/pull to a remote repository so that my website's files will be updated by my push.

How can I create a remote repository that also includes all of my projects folders so that I can push from my local repository and the remote repository will get updated with the new files/folders I create in my project locally? How does Git handle transferring files?

As of right now, I have tried creating a new repository on the remote server and pushing my local repository to it. It successfully pushes to the repository (updates commits), BUT I can't get the actual files (.html, .php, .js, etc.) to the server through the push.