Get a decent demo package together. A demo package should include a one-page biography, a professional demo CD, a photograph of yourself and any press clippings you may have about yourself. Keep a demo package with you whenever you gig--a potential agent may be in your audience.
Research every artist and repertoire representative (A&R rep) you can find. Discard the information of any who do not represent your style of music--while you may think your music is good enough to win them over, they will more than likely throw your demo package out if they don't feel they can represent it. Do not send unsolicited demos to A&R reps who say they are not accepting demos--these too will be discarded.
Verify all your information before sending a demo package to an A&R rep. Check that you have addressed the package to the correct person, address and department. Double-check that they are accepting demos and represent your style of music before sending.
Have a full repertoire of songs ready to audition. Make sure you are well-practiced in each song and that they represent your style. If an A&R rep likes your demo, she may call you in to perform some more music for her.
Get a good entertainment lawyer if offered a contract. Have them check the contract to make sure that the terms are reasonable and the royalties fair before signing anything.