The guide at that URL is kind of messy. I can't really figure out which of parts of it apply to my case, i.e. which configuration files I have to create/modify.
What are the steps I need to take to get the mentioned setup to run?
Try installing, configuring and running Alfresco using the Alfresco-installed Tomcat. Once you understand the configuration overrides (with the help of the Wiki page mentioned), you'll be able to apply the appropriate modifications to your own Tomcat instance. There is a good book and courses available as well.