I tried installing homebrew for about 3 days following the completely identical howto postings out there (i.e. “prefix with ‘arch -x86_64′”). Alas, it didn’t work:
$ arch -x86_64 /bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install.sh)" Password: Homebrew is not (yet) supported on ARM processors! Rerun the Homebrew installer under Rosetta 2. If you really know what you are doing and are prepared for a very broken experience you can use another installation option for installing on ARM: https://docs.brew.sh/Installation
The other recommendation (run the whole terminal under Rosetta2, scroll down to “Running a special flavor […]”) also did not work.
What did finally work though was changing my login shell to /bin/bash instead of the default zsh for the time being:
Maybe that helps someone.
The “install the M1 version” process described by Noah Peters (thanks, really!) did work on the first try.