Publishing jobs are not as few and far between as many people believe. While it's true that the vast majority of publishing jobs were once located in New York City, today there are any number of opportunities in other states, as well as online.
Establish yourself with qualifications. Jobs in publishing are not as scarce as they once were, but there are still some stringent skill requirements.
A degree in English, communications or a related field of study is most helpful. If that isn't possible, taking a few classes would also be helpful. Doing the appropriate reading on your own is an excellent way to get some experience and expertise, even if you do have the degree. Keeping current with publishing changes and trends will keep you ready for job interviews.
Work your way up. If you have your eye on a cherry publishing job, you may just have to start at the bottom. And that may not be as an associate editor - it may be as the coffee fetcher. But if you keep up with the industry and are good at whatever job you do get, it will be much easier to move up the ranks into the "real" publishing jobs.
Have an excellent resume and include clips. Even if you have the qualifications, you will need to have some published editing or writing samples. If possible, they should be published samples of works you have edited, and they should be relevant to the publisher's business. If you don't have any published samples, it will be very difficult to get your foot in the door in any capacity.
There are ways to get samples if you don't have any. One way is to offer your services for free to non-profit companies, for church newsletters, or anything else that is likely to take you up on your offer of free work.
One way to get more prestigious clips is to do an internship with a newspaper or magazine.
These publications generally take in a lot of interns, and their clips will carry a little more weight than a newsletter.
Take the time to choose your prospective employers. By researching a few publishers, you may find some that you believe would be a good fit. These would be good places to place cold calls and ask for interviews. By knowing a lot about the company and what they publish, and having a good pool of related clips, you have a much better chance than if you simply sit back and wait for jobs to become available.
Search online for jobs. There are publishers now that exist entirely online. These include ebook publishers, ezine publishers, and many other types. You can search for "publisher jobs" or even just "publishers" if you want to place a cold call. Some publishers have both an online and a brick and mortar component, so it doesn't hurt to be familiar with both.
Jobs in publishing can also be found by searching through writing market books, such as the Writer's Market or the Novel and Short Story Writer's Market. These sources may send you in new directions you would never have thought of.