“Selling yourself” may sound kind of harsh, but if you are a freelance writer you should keep in mind that you have to know how to promote yourself. It is not easy to “sell yourself” if you don’t have writer’s background, because if you want to get job you should show what you have already achieved in the sphere, like clippings, references, etc. But quite often writers complain that they cannot promote themselves even if they possess enough experience and expertise.
If you are a writer of such kind, it means that you have a circle of employers or editors who have already published your works. That’s a good point to start with! Ask testimonials from them and along with clippings those testimonials will assist you in self-promoting. Word-of-mouth marketing doesn’t require putting great efforts, because you just have to communicate efficiently with your employers, clients or editors.
Many writers create their web sites and promote them. That can bring good results as well. But if you lack communication skills with those who already read your writing and praised it your personal web site will hardly compensate possible fruits of communication.
What do you think of word-of-mouth marketing?

Wanted to add some points to what I previously said about "word-of-mouth" marketing. Actually, I consider "word-of-mouth" marketing to be one of most efficient ways to market yourself, but in this post I wanted to emphasize that writers don't have to neglect online self-promotion. And what I mean here is not only creating your own web-site, although it's a good idea, but active participation in online writing communities. Blogs, forums are the places where you can introduce yourself, share your experience, get a huge amount of useful information and find potential clients!
If you want to learn sth new about this or that company or publisher, you might also ask other writers and get a comprehensive response. If you want to get a feedback to your pice of writing, forums are great places as well.
What I mean is that communication through forums or blogs with people who have similar professional interests to yours can turn very-very fruitful!

You are right.
Brilliant phrase! 

Good inputs.

However how should one start if one does not have a writer's background but nonetheless can write very well?

Such a writer cannot produce any testimonials or clippings so how can he or she sell himself/herself?