A few times a week, I take calls with college students and young professionals who want to work in the music industry.
My first piece of advice is simple: Don't.
To explain, I call upon the idea of "blue ocean strategy," which supposes that you can make high profits by creating new demand in uncontested markets. Put more simply, if you go fishing where no one else is, you'll find a clear, not bloody, water and walk away with more fish.
In the context of your job search, this means looking for opportunities where other people haven't thought to go yet.
If you want to start working in the music business, the obvious options are obvious to everyone else, too: record labels, music sites, booking agencies, etc. Because of the high demand for these positions (coupled with your lack of experience), you won't have much leverage in the negotiation and might even have to accept an offer (like an internship with possibility of full-time employment) without pay. Later, if you find yourself unhappy or suffering under a bad manager, you'll likely be reminded how many people wanted your job. (This is, of course, unfair to companies that have great entry level opportunities, but I've heard some pretty terrible stories over the years).
Instead, you can get some fantastic experience (and a better salary) by looking in non-obvious places.
I saw how valuable this could be when I was in college and interning for the ad agency BBDO. I was assigned to the account management team for Cingular Wireless and got to see all aspects of the agency and how it worked with its brand clients.
I also expressed interest in working on Cingular's music initiatives. Though it was a small part of my job, I got to help the senior account managers and a major record label put together a plan for bringing Cingular's ringtone platform to market. Since BBDO didn't have an in-house music team, all I had to do was raise my hand and say, "Can I help with this?"
When I started applying to other music-related jobs, that was a great talking point and something I could highlight on my resume. Yet I also walked away with functional experience that was relevant to any advertising or marketing job. It gave me more options rather than tying my skills to a very niche industry, and that is especially important in a tough economy.
If you want to get started in the music business, take a look around for opportunities other people don't see... maybe that's working for an agency, like BBDO, or for a consumer packaged goods company, like Coca-Cola, which has so many ties to music and entertainment. Non-profits and universities (which book talent for fundraisers and events) are other good places to look, so long as you have an idea of where you can help.
However, if you find yourself stuck in a cubicle with no way to work music into your daily tasks, make an opportunity for yourself in your spare time. There are thousands of bands looking for help with marketing, management, PR and the like, but they often can't afford the help. Read Donald Passman's book and find a project you can work on pro-bono work in exchange for the experience. It will show potential employers -- whether in the traditional music industry or not -- that you are serious about your dream, even if you're currently an accountant.