Odoo's official process has seven steps, and it is the same idea on every hosting type: test first, fix, rehearse, then upgrade production.

The steps

• Request an upgraded test database: on Odoo Online from the database manager (Manage, then Upgrade, purpose Test); on Odoo.sh from the Upgrade tab on a staging branch; on-premise with the official upgrade script and the test option.
• Upgrade your custom modules to the target version: install them on an empty database, fix errors and write upgrade scripts in the upgrades or migrations folder for any data changes.
• Test the upgraded database: views, reports, record creation, website pages, integrations and full business flows. Test databases are neutralised, so emails, payments and scheduled actions are disabled.
• Report every problem to Odoo support at the migration stage and request a new test database after each fix.
• Plan the go-live at a quiet time and run a full rehearsal the day before.
• Request the production upgrade: purpose Production on Odoo Online, a new commit on the production branch on Odoo.sh, or the upgrade script with the production option on-premise.
• Report any post-go-live issue at the production stage.

Good to know

• The database is unavailable during the production upgrade, and on Odoo Online you cannot go back once it completes.
• Custom modules block the upgrade until they are compatible with the target version.
• For Enterprise, the upgrade service is included; in-house or third-party modules without a maintenance contract are your responsibility.
• Community users usually upgrade with the OCA's OpenUpgrade project.

Always check the current official upgrade documentation for your target version, since commands and menus can change.