One of the newest jobs in music, or almost any field for that matter, is new media. In fact, because of the increasing importance of technology, it is probably one of the fastest growing careers in the music business too. So, here's some info on what a new media career might involve.
What they do:
New media is exactly what it sounds like: working with any forms of media that are new. This could mean working with direct to fan marketing, social networks, widgets, youtube videos, mobile, etc. At the lower levels of this career it can be extremely tedious and often requires lots of updates social networks. It also involves good people skills and an ability to build relationships with contacts at different sites and write messages (copy) that appeal to fans of each artist.
This can range depending on the company and the specific job but generally should know at least basic html, css, and photo shop. You should understand how to build a following online and help and artist engage existing fans while attracting new ones. Some jobs require more advanced web design knowledge including flash, PHP, SQL, etc.
How to get experience:
In some ways this can be the easiest to get experience in: learn the applicable codes and programs, build your own social networks and get a following for yourself. This shows places you apply that you know what you're doing. However, online marketing and planning for a band is a bit different than for a person or other brand so use that self-built experience to get an internship.
This job will likely continue to evolve drastically over the coming years. If you want to work in this field it will require a knowledge and interest in culture, new technology, and media trends. You should be the kind of person who find the newest thing online before your friends. For instance, the first of your friends on FourSquare or the one who was on Twitter when your friends all thought it was useless.