Setup of German style is no longer different than using upstream OpenStreetMap carto style thus just refer to INSTALL.md for usage instructions.
However if you want latin script osm2pgsql version 1.8.0 or higher is required.
To create a database with latin script names use
openstreetmap-carto-flex-l10n.lua instead of the one from upstream.
This will also require the installation of the osml10n software.
See osml10n installation instructions for details.
If you want to change the target langugage from German to another language
using latin script change the 'L10NLANG' variable in
openstreetmap-carto-flex-l10n.lua from 'de' to your desired language
e.g. 'en', 'fr' or 'es'.