Make a demo recording. Doesn't have to be flawless, just done well enough that the publishers can visualize what the perfect production would sound like. Send it to one of the publishers on the web page below.
Keep a dated copy for yourself and print out the words with something like, "On this date I heard a copy of [name of your song] by [Your Name] and have witnesses who have listened to the song sign it to protect yourself.
Don't forget, music is a business. You may get offers that say the song has potential but needs some changes. If you approve the changes, they become co-authors and get part of the royalties. Sometimes that's a tough choice to make for someone just getting started.
If they want you to pay to publish your writings or songs, that's called "vanity publishing." Unless you have a lot of money and just want to see your creation in print, I'd pass on that. If you create a really good product with commercial possibilities, it should stand on it's own financially.
List of Country music publishers:
http://www.song-makes-musicbusiness.com/Nashville-music-publishers.html