Both answers so far are good. Especially the info about having great songs.
I think it's so competitive out there that my suggestion to you is to focus on developing relationships with artists you believe in. If you write songs with them and they value your writing contribution, you will have a chance that they will cut your song or songs. Yes there are song pluggers and publishing deals. But ultimately it is about the steps you take to become good at what you do and to be proactively selling them in a way that fits your brand and isn't too pushy. And it's about becoming of value in the co-writing experience.
Unless of course your songs are insanely amazing. Actually even when they are, you still need believers to want to cut them.

You have to go where successful artistes are. One of such places is a PRO, performance rights organisation. They usually have events and platform for collaboration, at least ASCAP does. you'd have to be a member though. Here's the link to the annual event and the ASCAP Collaborator's Corner: http://www.ascap.com/expo and http://www.ascap.com/collaborator/. Go for maximum success. Good luck.

More times than not this would involve cowriting with the artist themselves. You could also hire a reputable song plugger to pitch your catalog. However this comes at a price. Getting signed to a publishing deal that has relationships with artists and labels is another way to go but like anything worth having is very competitive. I live in Nashville and the city is full of people trying to do this exact thing -- most of them of been at it for years. The last and most important ingredient of course is to write exceptionally good songs. :) Best of luck.