Know what is being updated.
List the WordPress, theme and plugin changes involved. Check which licences allow updates and whether custom code or a connected service needs attention. Keep a record of the current setup.
Check the backup includes the right things.
A typical WordPress restore needs both the files and the database. Establish when the backup was made, where it is kept and how it can be restored. The presence of a backup job is not the same as a tested recovery route.
Use a suitable test copy.
WooCommerce recommends testing updates on a staging site before applying them to production. A test copy also needs its mail, payment and connected-service behaviour configured so it does not send real customer messages or create live transactions.
Check the journeys that matter.
For a service site that might mean the contact form and booking link. A shop can need checks of products, basket, checkout, payment methods and order handling. Agree the test list for your website before starting.
Plan the live change and the rollback.
Choose an appropriate change window and identify who applies the update, checks the result and handles any problem. On a busy shop, discuss how new orders or changes would be treated if an older backup had to be restored.
Official reading
WordPress: backupsWooCommerce: how to update