Record a music demo. Record it in the best studio than you can afford and on the best equipment available. Hire a good sound engineer and mixer to make sure that the quality of the demo is the highest it can be.
Get your demo to an A&R rep. These are the people who find talent and shop new acts to the record labels. While it is very difficult for new acts to gain the attention of label A&R reps, there are independent A&R reps who can be hired to work for you for an up front fee or for a percentage of any eventual recording deal.
Play your music live. Book gigs at venues that will allow you to perform regularly. You want to build up a local fan base.
Perform your music on tour. Perform in as many cities or states, even countries, as your budget will allow since this will help you expand your fan base beyond your home base.
Create a website and sell your music online. Every artist or band should have a website to promote themselves.
Make use of social networking sites to promote you music. Myspace, for example, is a social networking site that is full of record company artist pages. The site also includes many pages for relatively unknown acts as well.
Contact a publishing company directly. This is most effective if you create instrumental tracks. Ask the company if they have any top acts that write instrumental tracks. If so, agree to demo the tracks. Then approach the publishing company with the demos of the written tracks and try to sign a publishing deal.