Postgres minor version upgrade
Just do a dist-upgrade or the like on Linux, or install the newer versions on Windows/OSX. Minor versions ensure total compatibility with the data directory (heap, and index).

Stands to reason though, you'll have to stop the database during the upgrade.

From the official docs on versioning


  Minor releases are numbered by increasing the last part of the version number. Beginning with version 10, this is the second part of the version number, e.g. 10.0 to 10.1; for older versions this is the third part of the version number, e.g. 9.5.3 to 9.5.4. The PostgreSQL team only adds bug fixes to minor releases. All users should upgrade to the most recent minor release as soon as possible. While upgrades always have some risk, PostgreSQL minor releases fix only frequently-encountered, security, and data corruption bugs to reduce the risk of upgrading. The community considers not upgrading to be riskier than upgrading.


So essentially, PostgreSQL is so conservative that minor-version number upgrades are only issued when there is more risk to not-upgrading than upgrading. I've been working with PostgreSQL for about 15 years. I don't do any additional backups nor take any special precautions when doing minor upgrades. Not saying you can't -- even the docs say they come with "some risk."