Find online writing work and land the job
I am glad you asked that! One place to find online writing work is on my blog, Write and Get Paid. It offers daily posts listing interesting writing jobs I have come across for freelancers. I also encourage readers to send me information about any freelance openings that they know of which I've missed. Additionally, my blog has lots of information about using your blog to make money, doing social media work, and SEO for small businesses. There really is a wealth of opportunity online for a freelance writer if you know where to look.
Where to Look
Finding work is difficult at first, but quickly becomes second nature as you work through each day. You will be absolutely amazed at the number of opportunities you will hear about in the course of a day-- whether the source is a blog posting, an email, or something you come across in a news feed. I find many of the jobs I post in my email inbox daily.
Searching for online writing work is simple. Just type "freelance writing" into a Google search bar, and you will likely get similar results to those I did this evening: about 2,180,000 results in 0.19 seconds. (I was happy to see my website/blog on page one of the search results.) Perusing a few of the websites will point out some writing work that you can apply for. You can also do searches on job boards like Monster and Indeed, you will want to use 'telecommute' or 'any' for the location.
There are also a number of websites online dedicated to matching up writers and other freelancers with buyers that need their services. Examples of these are oDesk, Elance, and VWorker, and they can be great places to get started and find some regular clients. One tip on these boards: the pay scale will be decidedly lower than what you might make with gigs you find on job boards or from repeat clients, because there is international competition for the work. Do a good job on the projects you accept, and you will likely find clients returning to you frequently and willing to pay a fair wage.
How to Land the Jobs
As important as finding work is knowing how to apply so that you'll be taken seriously and considered for the jobs. Unlike most jobs you've applied for in the past, the buyers will not care about your job history or your education. They are solely concerned with your abilities that pertain to writing, so you'll need to be able to show them samples of your writing. If you do not have any, get busy and put together a few articles on interesting topics. If you aren't sure how to write a good article, or how to think of a relevant headline that will draw people in, do some scouting on the internet for tips. After you've read up on it, you will feel comfortable enough to put together three or four good pieces. Be sure that your grammar and spelling are correct, and keep your writing casual. Read your articles over before you send them, and even have someone you trust look them over if you aren't 100% confident.
Beyond your articles, you will want to tell the buyer why they should hire you for their specific project. If the writing project is about something you're expert in, tell them that! On the other hand, if it's a topic you aren't too familiar with, let them know that you are interested in the topic and look forward to researching it for the project.
Again, if it still feels all too foreign to you, go to my Write and Get Paid blog and look around. Check out some of the articles about writing well, some that talk about internet marketing so that you will be familiar with any terms someone might throw at you, and of course look over the job listings on my regular 'Freelance Writing Opportunities feature. Feel free to email me through the site if you have questions that I can help with.