How to get in a freelance writing career?

You can start by setting up your own blog and choosing a niche. You can write reviews on products, movies, restaurants or books you know. There are a lot of sites that offer free blogs nowadays. You can also submit articles in submissons sites like ezinearticles or ehow. The point of doing this is so you can have samples of your work published online you can show potential employers. The next step is to look for employers. This you know how to do, I presume? Make sure you have a well-written resume that summarizes your skills and experience as a writer. You can also provide the links to your blog or any articles you wrote and published online so the potential employers can get an idea what you have to offer.

There are also potential employers that may give you a writing test. They'll give you a topic plus a set of instructions to see how well you write. 

Make sure that you keep to the deadlines clients/employers give you.

Hope this helps. Good luck.  :)