The country music industry is very big and breaking into it is similar to breaking into any other music genre with one exception. Country music places a very big value on songwriting. In hindsight, this may seem obvious; country music is all about the words so songwriting would be the obvious thing to get into. This is a fact and if you are interested in this career path you can do no worse than starting out in the country music capital of Nashville.
When you arrive there, do not have any pretenses about making it big on the first day. It is not going to happen like that. So get a job. Try to find a job in one of the big publishing companies but do not reveal your aspirations to be a songwriter. Get hired, establish yourself as a good employee and build up your relationships with all the right people there. Then you can mention your abilities to them and get their help.
Get into the Nashville Songwriters Association International (NSAI). This organization will help you develop your craft and improve your talent. Then get involved in the local talent scene. There are a few venues that have open nights where you can display your talents. The talent scouts regularly visit these gigs and you just might impress someone enough to kick start your career.
Become a member of ASCAP, BMI, or SESAC. These organizations are responsible for collecting your royalties. But keep in mind that you can be a member of only one of these organizations, so choose wisely. Be patient, keep plugging away at it and eventually your efforts will be rewarded.