When it comes to website hosting/design, I have a theory that there are actually three different types of people.
First level knowledge: This would be users who are able to use "auto setup" programs such as fantastico , use this to install scripts and can use CMS back ends, but really have no idea how the underlying scripts work. Most beginning website owners are at this level when starting out, and generally pay someone else to manage their websites if they need more advanced management or do not have the time to learn/manage a website.
Second level knowledge: This is generally being able to setup webpages, some familiarity with different server technologies such as php, mysql, html, asp (or asp.net if learning windows), html, and so on so on. At this level of knowledge, if you are proficient, you can install just about any script without needing to know how exactly the server itself works. Most web designers eventually build up to this level of knowledge.
Third level knowledge: This involves knowledge of not only the above, but also knowing about such things as DNS zone setups, Operating system installation/upkeep, in short being able to take a computer that has a base operating system (such as CentOS), connect to it from a command prompt, and then be able to set such system as a webhosting server. Knowledge of linux/windows command line / server software is generally needed. This level is where the majority of technicians who work for web hosting companies are at.
Of course everyone has their own ways that they learn. I have seen some people take classes in colleges to learn how to do some of the above, while others started out by initially setting up websites (level 1) and then learning what is possible to learn on a shared hosting server, then go to the next level by building locally based computers and experimenting with them to learn more on how webhosting works.
If learning on your own, you would need to decide at what level you would want to be, then proceed from there.
Starting out, I recommend reading :
http://www.amazon.com/Building-Site-Dummies-David-Crowder/dp/0764571443 (good for level 1, going into level 2)
Once ready and the first 2 levels have been met, I would recommend possibly checking if your local community college provides any classes in website / server management.
Course all of the above is just a theory, everyone is different, has different levels of knoweledge, and its entirely possible to know a little bit about each level while not "specializing" in each.
I myself started out as a computer hardware tech, setup my first website not having any idea what I was doing, then started learning the ropes. Once I had an acceptable level of knowledge, I applied with Lunarpages, got a level 1 position, and over the last 3 years learning even more.
I still learn something new almost every day.
When it comes to learning tech end of things, its an ongoing process as the technologies change, so if you are going for becoming a server technician, you will allways be learning.