Record mastered, studio-quality demos of your songs. Hire a professional recording engineer/producer with the skills necessary to turn out radio-ready versions of your songs. Hire session vocalists and musicians who can capture the feeling of your songs with a commercial, modern production.
Network with music publishers, record labels and recording artists. Make yourself a presence at workshops and seminars, and let people know your aim is to cut professional songs.
Register with a performing rights organization like ASCAP, BMI or SESAC to ensure that you receive performance royalties when your music is played.
Submit your demo along with a bio and cover letter to music publishers, record labels, producers, A&R executives, music supervisors and other industry professionals you feel might have a use for your music. For example, if you write country music, you might want to send your demos to publishers in Nashville. If possible, hire a lawyer and/or manager to represent you and present your demo to these professionals.
Negotiate contracts with parties interested in your music, making sure that you get a songwriter's share and a share of the publishing.