It's actually pretty easy: just do the job. Open your own blog and write. Cover whatever beat you are interested in. You'll have almost no audience at first, which is normal, but ignore that. Write as if you had your dream job.

Then, you can start submitting some of your writing to more serious blogs and news organizations. Work your way up slowly. For instance, to make it to the New York Times, start with being "reprinted" in Business Insider, then HuffPo, then NYT.

PS: be aware that there is very little money in journalism. As in, ridiculously no money at all. You can work really hard day and night and make $30K/year. Or write a php website and make 4 times more.