First I created an empty git repository in the public html folder of the domain (This assumes that you have ssh access to your server). Also, I made an initial commit there.

$ cd /path-to-your-domain/html
$ git init
$ git add .
$ git commit -m "First import"

Then I placed the HUB outside the public html folder, not in the home directory as Andrew J. Flemming suggested. I created a folder called repo which sits inside the domain folder. Inside repo, I added another folder called your-domain.git, which will host a bare git repository (notice that you can call this folder any way you want, as long as it ends with .git, your-domain.git is just a placeholder in this case).

$ cd /path-to-your-domain/
$ mkdir repo
$ cd repo
$ mkdir your-domain.git
$ cd your-domain.git
$ git --bare init

Our PRIME repository needs to have a remote repository in order to get the files that are part of the website, in this case the folder we just created your-domain.git will act as the remote.

$ cd /path-to-your-domain/html
$ git remote add hub /path-to-your-domain/repo/your-domain.git
$ git remote show hub
$ git push hub master

Then we just need to add two hooks. These will tell the repositories that we created what to do once they receive new code. Two hooks are needed: a post-commit, and a post-update. The post-commit, has to be created in the .git/hooks/ folder of your PRIME repository. We can do this by adding the following code the post-commit.sample file and then removing the .sample part to activate it.

#!/bin/sh
git push hub

If you don't have a post-commit.sample, just create the post-commit file directly and add the previous bit of code.

Now we need a post~update hook that will reside in the your-domain.git/hooks/ folder. This will tell our HUB to go to the PRIME repository and then execute a pull from that location for us.

#!/bin/sh
cd /path-to-your-domain/html || exit
unset GIT_DIR
git pull hub master
git-update-server-info

In my case, I had some code in my local repository already since I wanted to test how the website would look before deploying it to the server. Then I just had to add a remote to the local repository as follows:

$ cd /path-to-your-local-repository
$ git remote add hub ssh://yourdomain.com@yourdomain.com:/path-to-your-domain/repo/your-domain.git
$ git pull hub master

Notice that in the previous code, the line ssh://yourdomain.com@yourdomain.com: assumes that you have a username (part before the @) and the address of the server you want to access (what comes after the @).

Finally, I was able to push the site I built locally to the server using these commands:

$ git add .
$ git commit -m "Initial commit of my website"
$ git push hub master

The same procedure can be used for other domains in your server as long as you define a HUB for each of them.