There’s a great recipe for this at Using Git to manage a web site. I thought I’d share my version of it, just slightly modified from the original and HostGator-centric. Even if you’re using shared hosting, you may still be able to use git to remotely install updates to your sites.
I was pleasantly surprised to discover that HostGator DOES include git in it’s shared hosting packages. You’ll need
ssh access for this recipe to work — an extra hoop for HostGator customers using shared hosting.