I have a few VPS based on Ubuntu and I have an alert on my calendar to login from time to time and update the packages and keep up with security fixes.

Here’s the sequence I use (it’s mostly a note to myself for the next time I forget)

Connect as root to the server, then you run:

apt-get update

to get the packages index updates.

Then run:

apt-get upgrade

to actually update the packages.

Then, if needed (depends on the kind of packages that needed an update), reboot the system:

reboot