There are dozens of books that explain all the ways to research and contact a publisher. There are many resources that list publishers, some accept unsolicited material - most don't. There is a cost - but it should never be an up front cost (anyone that wants money up front is likely a "song shark" rather than a publisher). In most publishing deals, the publisher gets part of the royalty fees (in my case 50%).
Normally you must contact a publisher (hopefully you've done research to make sure the publisher works in the musical genre you do best) and determine if they accept material. There is a whole mating dance that is involved - which I choose not to get into, but the information is readily available.
All I can say - if you are really, really, really serious about being a writer - you will do your own research.
I've worked with a few publishers over the years most of which I accessed by use of the traditional mating dance. However, the publisher I currently work with actually came through Taxi (for those who bash Taxi - it can work). A writer I worked with was a member. A song we co-wrote was submitted to Taxi, Taxi in turn submitted the song to this publisher, publisher placed it in a movie (we did have to re-record with better vocals, a better mastering job, etc). Now there were many other songs Taxi passed on and once we/I had direct access to the publisher there were many songs he passed on. That's all part of the dance.
The writer I worked with has moved on (he is reportedly now working with some people in the Tim McGraw/Faith Hill camp). I stayed with the publisher because my long term goal has always been composing for film - and this publisher has a track record in that genre. He has since placed a song in another film and ABC just picked something up for some TV special. The songs in the films are just background filler (no closing title "featured material") - but each small success paved the way for the next success.
When you work with this type of publisher (actually most publishers) you have to write very commercial 3 minute songs, heavy on good lyrics, clever melodies and all the other "formula driven guideline" (things that so many on this board seem to detest). However, everytime I get checks in the mail (from the publisher and from BMI) I can forgive myself for writing "formula driven songs"