Backup your files and database.
# stash any local changes in your site that aren't committed yet
git stash
# fetch the release you want to update to, ie: 8.02
git fetch origin v8.02
# update the code in your site with that release
git rebase v8.02
# restore your local changes
git stash pop
Make sure the folders that need to be writable are writable by the web server