HMC update/upgrade process is pretty simple.
You can view the current version in using help button in menu.
The latest versions are available for download on the Fix Central
https://www.ibm.com/support/fixcentral
It is recommended to make a backup before installing the fix. In this case, the backup will be on a USB flash drive.
The backup itself can take quite a long time. In this case, 40 minutes.
The actual HMC update is started again via the Console Management menu.