Record at least three of your most promising songs in a professional studio and/or with a competent recording engineer. Choose your most marketable songs, avoiding long intros or solos, unless your genre calls for it. If you are a non-performing songwriter, hire professional session musicians to record your music.
Build a press kit. Include a bio, press clippings, cover letter stating the intent of presenting your demo and the demo CD itself.
Contact music publishers, producers and record labels that work within your specific genre. For example, if you write country songs, look up industry contacts that specialize in country, many of which would be found in Nashville. Ask if it would be acceptable to submit your demo/press kit for consideration.
Submit your press kit to the industry you contacted. If possible, hire a lawyer or manager and have them submit it on your behalf.
Attend industry functions (seminars, parties, shows) and make connections. Talk about your music. Hand out your demo to interested parties.