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 the app in your applications folder.
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.