Qualifications
This is one job where a college degree may or may not be necessary. That B.S. in computer science probably looks great hanging on your wall, but it doesn't mean you're qualified to manage a major computer network.
Education and skill can be very different things, and the network administration world is a good example of this. Network admins require not only a serious set of smarts, but also terrific organizational and management skills and a dogged work ethic.
It'll depend on the company, but often enough, employers will want you to have some specific IT- or information security-related certifications. These certifications all sound arcane and have names like MCSE, CCNP, RHCE, CWNA, GSEC, GCIH, CISSP, Security+, CCIE, CISM, etc. No, we're not going to spell out the whole alphabet soup of acronyms for you. Put down the Xbox controller and show some initiative.
There are study guides available for a lot of the IT-centric certifications out there. Pretty much all of them require a test, and there can be a hefty price tag for just taking the thing, regardless of whether or not you pass. No joke.
If you already work in a major company's network administration department, you might be able to attend classes and take tests on the company's dime. You can at least ask—companies are often open to helping their workers educate themselves, so long as it'll benefit the company in the end.
The upside is, the more certifications you have, the more marketable you are. The downside is, many of the classes cost upwards of $4,000 each. If you can convince your boss to fork over the cash, good for you. But you'd better pass—if you get our drift.