You can actually use a bash script with ssh for that. I've tried it and it's awesome. The script would look something like this:
ssh user@myserver.domain << EOF
git fetch # get the code
git checkout COMMIT # checkout the desired commit
cp ... # copy some configuration files or whatever you'd like to do
service nginx restart # restart your services or reload configurations, etc
EOF
This is overly simplified of course. I just wanted to give you a simple snippet to get started. I'm assuming you do know how to ssh into a machine (and have permission for that). Well, in the end, you will endup with a simple script that just updates everything for you. As easy as:
$ run/deploy
And yes, I like to save my scripts in a run directory :p