There are many employers of varying sorts. You can go freelance and find individual assignments, or you can find someone who needs your writing skills regularly. There are advantages to each option, and it can very much so be a matter of personal preference. Publishing your own work has become incredibly easy. Many people earn a living writing for their own website, whether in blog form or otherwise. The earning potential varies tremendously, depending on topic and your own skill at monetizing a website. But with the right software you don't have to be a great website designer or constantly pay someone to maintain your site for you. All you need is to get set up and go.
There are also many opportunities in writing for others. Many website owners would sooner pay someone else to do their writing, whether it be writing articles for their site or sales copy for their product. You bring the skills; they tell you what is needed. It's easy to work for low pay online. There's a lot of competition out there, and many writers willing to work for a pittance. It can be hard to get serious pay as a writer, but it is not impossible. Show your quality and know that you are worth it. If you're helping people earn a better living, they will know when you're the writer they need to keep using. In many cases, having your own website is strongly recommended.
It's a way to show off your work and attract clients if you're freelancing. A good website is a major part of your presence on the web. Even if you don't expect to do a lot of marketing online, listing a website on your business card is just one more sign of being serious and professional. There have rarely been more possibilities for earning a living as a writer. Not all writers will succeed, and not all styles of writing will appeal to people online. But if you can adapt you will give yourself more chances to build a viable business as a writer.