Mautic is only a glorified PHP web app. You could use any PHP web app tutorial and replace mentions of the other app with “Mautic”.
The key for a fast and reliable server is always the servers’ configurations. It need to be based on the underlying hardware.
Anyways, there goes what you need to focus on: a fast CPU and fast storage.
You could use for a control panel such as DirectAdmin to make it easier on you in regard to the server install, configuration and management.
About the CPU and RAM:
PHP is single-threaded. Each visitor will take one thread. And each PHP run will require RAM.
So, depending on your traffic, you may need more CPU threads and RAM.
Other than that, this is how I’m installing it on any web server:
download the archive
unzip it
create a DB schema w/ the user/pass
and point your browser to the domain used for your install.