I would guess proving yourself to a potential employer would be very similar for the two fields. The most important thing being your portfolio of work. Other factors that could help you would be education, references, and experience.
Students in advertising generally do a book of ad concepts for either existing companies or for a theoretical company in a particular industry. You could do the same fairly easily if you don’t have something similar already, or to add to it. With your media experience, you have a real advantage. Take a company you like and take their advertising in a new direction just like you would if they came to you at the agency. Record a couple 15 second radio spot ideas or put together a website and suddenly you’re getting all multi-channel (or whatever the buzzword is). A friend of mine who’s on the creative side of advertising mocked up some print ad concepts for a local company and took them by their offices, he was able to get in to see their creative director and get some feedback on the work he’d done. Once you get a couple pieces of work together, I think it’s fairly common practice to get some decent prints made up and put them together in some sort of snazzy and professional physical portfolio.
As far as getting the interview and breaking into the field, you may already know a lot of folks who could help, but I’ve had a lot of luck with local groups who get together to learn and network for a particular profession. Meetup.com is a good source for groups, Upcoming (upcoming.yahoo.com) is another and writing an email or going by a local university can usually net you a list of good resources. (Sometimes the people in the department are a little more friendly/knowledgeable and a little less overwhelmed than central admissions or a help desk). Also, depending on what specific area you’re looking at there’s usually some sort of accreditation body that may have meetings as well, of course I’m drawing a blank right now, but they love advertising in trade magazine, so Borders may not be a bad place to start either.
Getting long winded, so I’ll quit now. I wish you luck with the switch.
Zach