In most cases, you can just provision the OS from a web interface. If you get a bigger machine where you need to configure the disks yourself, there is a pretty easy to use command line tool they built which does most of the work.

The only part which I had to learn the hard way is configuring iptables to secure my servers against external attacks. Luckily, recent versions of docker make it easy to keep iptables configured - at the beginning, that was almost a nightmare...

Is there a command line tool to automate installing the OS?

Well what I would really like is to be able to deploy something like an "AMI" on these dedicated servers. Any ideas for how to get something close?

Yes, there is one: https://wiki.hetzner.de/index.php/Installimage/en