Are there any good "Getting started with Tomcat" documents/tutorials/sites?
The official docs are horribly written and jump from the intricacies of compiling Tomcat to how you should lay out your site on disk.
Specifically I want to get Tomcat serving through Apache httpd.
Regarding the running Tomcat behind Apache, you need to use either mod_proxy or mod_jk. I believe the first one is preferable, so this is a bit outdated how-to.
This is a tutorial for configuring mod_proxy on httpd's side. In tomcat you only need to enable an AJP connector:
<Connector port="8009" protocol="AJP/1.3" redirectPort="8443" />
Here are directions on how to configure it.
I did a fair bit of work with Tomcat at my last job which unfortunately I don't remember much of but I would suggest searching/posting on the Tomcat users mailing list (http://tomcat.apache.org/lists.html). I do at least remember they were quite helpful for a few problems.
Finding good documentation on Tomcat is challenging; the official docs are mediocre at best as you point out. Moreover, each version of Tomcat changes significantly from the previous version making up to date documentation difficult to maintain.
The best documentation I have found on Tomcat is the Wrox title: Tomcat 6.
It addresses the Apache httpd issue.
The best source I've found for deep understanding is a book called How Tomcat Works. There's also an O'Reilly title Tomcat: The Definitive Guide for more of a "how to" approach.
Once you've got a good handle on the Tomcat basics, I've found that this config generator is helpful when configuring AJP connections. (You can determine the "Apache mpm" parameter by executing apachectl -l, which lists compiled-in modules.)