Write your song and make a recording of it being played. Get formal, professional-looking copies of your music made for distribution to publishing houses.
Copyright your music. On all copies of your music, add the copyright symbol, the year of publishing, and your name, so that it looks something like this:
© 2009 by John Smith
You could also do what is called a "poor man's copyright," where you mail a copy of your music to yourself via certified mail and keep the envelope sealed in case you're ever charged with plagiarism. However, the safest way to copyright your work is to register it with the United States Copyright Office. Go to their website and either file online (which will cost you $35) or download and print out form SL-35 and mail in your submission (this will cost you $50).
Post samples of your music online, either by creating your own website or using a website such as MySpace. This will help expose your music to more people.
Gather a list of publishing companies and get contact information for them. The easiest way is through their websites. This will also allow you to research the publisher and see if they publish your type of music (no sense in sending your punk song to a publisher of gospel music). Contact the publisher, providing a sample of your music and a link to the site where you have your samples posted.
You should send copies of your music to only one publisher at a time as a professional courtesy. If the publisher rejects your song, you can move on to the next one. This will prevent situations where two different publishers accept your proposal at the same time (plus, most publishers forbid you to submit your music to another publisher while they review it).
Register with a performing rights organization such as BMI or ASCAP. You'll have to research each group to see which one is the best fit for you personally, but John Buckman of buckman's magnatune blog recommends ASCAP because it's free to register with them, you're not locked into a contract for as long a time as you are with BMI, and you give up fewer rights to your music to ASCAP than to BMI. But again, you need to decide which one is the best fit for you.
If there isn't a publisher who's interested in publishing your music, form your own publishing company and publish it yourself.