I moved up the ladder. Out of University with a Pschology degree, I got a job with a local ISP in Ottawa. Being with a small company just as the Web became a "Big Thing" sure makes you learn fast. When you do a bit of everything to the company (accounting Perl scripts, sysadmin, web authoring) you tend to run to keep up. You learn even faster when the hard-drive on your main server dies in the middle of the night...
After the company disappeared, I moved my O'Reilly books cross-town to a government department, and worked with a few more people doing web admin with a bit of system admin thrown in. After two years there, I graduated to the local Unix Support group. Today I help support 150+ Unices, with a few NT boxes thrown in for flavor. A work with a talented group of people, whom I try to learn as much as I can from.
How did I do it? I did a bunch of self learning. It may be a cliche, but cracking open an O'Reilly book, and walking your way through a problem really worked for me. Plus, in the beginning I had the good fortune to have a Senior Admin with alot of patience for all my questions.
The first language I learned was Perl. I have found it to be an invaluable tool for me. I have since found PHP a help with Web apps, and MySQL for db work. However, your Milage may vary. Select your tool with the job in mind.
In general, find what you enjoy to do, and the appropriate job will find you.
