Postgres.app 2.0 or later has an automatic update function. Just open the app, and select "Check For Updates…" from the "Postgres" menu.
If you want to convert a data directory to a new major version (eg. 9.5 to 9.6), see migrating data.
From Postgres.app 9.5.x.x or 9.6.x.x
You can upgrade to Postgres.app 2 just by replacing the the app in your applications folder.
- Quit the old version of Postgres.app
- Download the new version of Postgres.app
- Replace the old version in /Applications with the new version
- Double click. Postgres.app 2 will automatically detect the existing data directories if they are in the standard location. If you are using a different location, add them manually by opening the sidebar and clicking the plus button.
From earlier versions of Postgres.app
If you want to upgrade from earlier versions of Postgres.app, you will need to migrate your data.
Alternatively, you can make a custom version of Postgres.app 2 that supports the older server versions. See this page for details.