Study the mechanics of popular songs to learn what makes them catchy and successful. Listen to hit songs from yesterday and today. You need to be hard-wired to write hooks and be up-to-date on what currently sells in order to compete.
Write marketable songs with good hooks as often as possible. You will become a better songwriter through trial and error, more able to weed out the non-hits. Set aside time during the day to focus on songwriting and/or write songs while you wait in line at the grocery store or while driving.
Record professional demos of your songs at recording studios, using professional session musicians and vocalists. In order to impress publishers, A&R execs and others looking for hit songs, you need to present your songs to pitch in a professional package. Record at least three of your most promising songs.
Network within the music industry to establish connections with people who might want to cut your songs. Attend seminars, workshops, shows and more and talk to people with sway in the industry. Small connections could lead to promising leads down the line.
Contact publishers, producers, record labels and other industry people and inquire as to whether or not you can submit your demo for consideration. If possible, hire a lawyer or manager to represent you, as your case will be taken much more seriously with a professional backing you.
Submit your demo to parties who agree to accept your demo package. Include a bio and cover letter stating the possible placement of your songs. For example, you might write that your songs would work with a "teen pop artist."
Negotiate contracts with parties interested in your song.
Repeat all of the steps above and hope for the best. A hit song is a combination of a great hook, the right artist, the right marketing and several other factors.