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.
You can upgrade to Postgres.app 2 just by replacing the app in your
/Applicationswith the new version
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.