I've had songs published and placed - in some cases placed on artist recordings and in some cases in movies and/or television. No major artists and only direct to video movies (no theatrical releases....yet). Each quarter I see some publishing checks and/or BMI checks in the mail. Not big bucks, but a few hundred here and there.
Ideally, you need to find a publisher that focuses on the genre you write best in. You need to contact a publisher in advance to establish rapport and determine in the publisher will accept your material, the format thay want, etc. It helps if you can write with specific artists in mind. Be aware, no decent publisher will accept unsolicited material. You can write an introduction letter with a brief bio, follow-up with a phone call, etc. etc.
You will be competing with some very good writers (perhaps some of the best) who have access to the best session players and singers - so, you better be real sure your material is well writen, well produced and most of all, pay for the best vocalist you can get your hands on.
Be prepared for lots of rejection - I've got a drawer full of rejection letters and even though I now have a couple of publishers that I have an in with, they still say no to most of what I submit (and I think after writing a couple of hundred songs, I'm at a point where I write some decent stuff).
There are a lot of good books on the subject and I suggest you do a lot of research so if and when you are ready to submit, you have a plan. I look at songwriting as a business (although I keep my day job - because trying to support oneself through music can often result in a slightly above poverty level existance). A person should not start a business or open a franchise without understanding the business - a person should not try to be a "professional" songwriter without knowing the business.
The Songwriter's Market is a good book that identifies publishers and what they are looking for, etc. How to Pitch & Promote Your Songs is a good book on the subject. Good luck......you'll need it!