One of the ways, that I find to be most convenient, for implementing what you are trying to achieve is to create a bare git repository in your remote server where you can push from git.
Following is how you can do it:
Make sure that you can SSH into your instance without having to type a password, that is. your public key is saved in ~/.ssh/authorized_keys
Step 1. Creating a repository on the server to mirror a repository that you would have on a local server.
$ mkdir web.git && cd web.git
$ git init --bare
Initialized empty Git repository in /home/ams/website.git/
Step 2: Define a post-receive hook
$ mkdir /var/www/www.example.org
$ cat > hooks/post-receive
GIT_WORK_TREE=/var/www/www.example.org git checkout -f
$ chmod +x hooks/post-receive
Step 3: On the workstation, defining a name for the remote server and then creating a new master branch there.
$ git remote add web ssh://server.example.org/home/ams/website.git
$ git push web +master:refs/heads/master
On the remote server, there should be a copy of your files in /var/www/www.example.org