If you are not familiar with git, don't worry about it. Just download the latest packet from moodle.org/downloads.
My normal process is the following:
Unzip the folder and rename it moodlenew. Move it /var/www
Then copy over config.php and any plugins that have been added to the moodlenew folder. You can check what plugins are installed on your Moodle site under SiteAdmin/Plugins. You just need to copy the folders over to the correct location in your moodlenew folder.
Once you have everything copied over, fix the ownership and permissions on the new folder. Back everything up (database and moodledata folder).
Then rename your exisiting moodle folder to moodleold. Rename your moodlenew folder to moodle. Open up a web browser and go through the install process.