One of the nicest things in git is that you can actually deploy code to production (or just your test environment) w/o implementing a complicated CI solution.
Off course that using CI such as Jenkins is recommended when compilation is required (JAVA/C/C++/C#) or when TDD/unit tests are use (and you better use them).
Yet, when you just need to deploy, git can be a great service for you.
Note: please note that you must an ssh access from the local machine (not always feasble).
Step #1: Setup a repository in the development environment and commit a first file
> git init
Step #2: Setup an environment at the web server
> mkdir /path/to/dir/website.git && cd /path/to/dir/website.git
> git init --bare
> git add index.html
> git commit -q -m "The index file was commited"
> git push web
It is a simple task, but tricky if you don't have a direct access to the server (anyone said Jenkins?)