I'm using cron-apt to do automatic apt update on my server. These are very simple steps on how to do it

1. Installing Cron-Apt from repository

# sudo apt-get install cron-apt

2. Edit config file

# sudo vi /etc/cron-apt/config
LOG="/var/log/cron-apt/log"
MAIL="/var/log/cron-apt/mail"
MAILON="always"

3. Make the cron-apt run on 8 am everyday

# sudo vi /etc/cron.d/cron-apt
0 8 * * * root test -x /usr/sbin/cron-apt && /usr/sbin/cron-apt

Please notice that this cron-apt is not running apt-get upgrade. But I'd prefer that way, so I can examine the available updates and choose when to run it. You can execute it using this command:

# sudo apt-get dist-upgrade