Listen to as much music as possible. This includes oldies and current chart hits. Listen to many different genres to expose yourself to different chords, melodies and songwriting techniques. For example, if you tend to write strictly rock music, listen to jazz or hip-hop to open your mind to new directions in your songwriting.
Write all the time, whenever you can. You can come up with melodies when you're in your car, at work or sitting on the couch. Set aside time every day to work on new songs and revise old ones. Treat songwriting like it's your job if you want it to be someday.
Network with people in the music industry. This can be as simple as establishing relationships with fellow songwriters. Go to open mic nights and music seminars and meet people like you, as well as others who already make a living writing songs.
Record high-quality demos of your best songs. The standard set of songs to send to a music publisher is three. Hire professional musicians to play your songs if need be. While a vocal/piano or vocal/guitar demo featuring the melody, lyrics and structure of a song is sometimes sufficient, in today's music world it is best if you submit fully-produced demos.
Contact music publishers who publish the type of songs you write and ask whether you can submit your demos for consideration.
Send a package containing your demos, a cover letter and biographical information to the music publishers of your choice.
Sign a publishing contract with a music publisher you choose who wants to work with you. Make sure you get your fair share of royalties and don't give up your rights.
Continue to write as much as possible and follow trends in music to make yourself a constant competitor in the songwriting world.