The best way to get under the hood depends on how much you already know (C programming helps a lot), and what you want to actually do.
My advice is to pick something to do with your computer, then work out how to do it.
Useful pointers: www.tldp.org
(the rather voluminous Linux manual)
(home page of the GNU operating system, often called “Linux”, and the Free Software Foundation)
(good place to find software)
(good place to develop software)