There is no room for error and 99 percent of employers in this field are looking for English writers. So, you either have to be a native, or be very fluent in English as a foreign speaker and writer (like it is my case). If you know that you are not a good English speaker you shouldn't consider this as an option. If you can write perfect English articles, the next thing that you have to do is go online and look for a freelancing site. There are a couple of very good ones with a lot of buyers (or employers) that you can find easily and those are the ones that you are looking for. The registering is free and the sites are very simple to use, so you should not have any problem with that.
Even before starting to look for projects that you can work on, it would be a good idea to have 10-15 400 word articles written as a portfolio. Choose different subjects for each one and base the articles upon using a couple of keywords in each one. Include one main keyword in the title as well and make sure that the title is interesting and intriguing so that any reader keeps reading the articles you write until the end. Make sure to use the keywords at least a couple of times, but do not overdo it as you can't have too many keywords in the same article.
After you established this portfolio (it is optional, but you will have more chances of getting a project) you can start looking for project that you think you can handle. It is a very good idea to actually have a small project at first but it is also important to provide with good quality articles so that the employer will give you some more. If you are really good and provide with the articles on time, the employer or buyer will keep working with you on a regular basis. Basically you will become their unofficial employee.
This is all that you need to do to become a freelance writer and get paid for writing. There are some things that you need to avoid. First of all, you have to avoid getting projects on subjects that you have never even heard about. It will be difficult to start studying about a particular subject and also provide with the articles on time. You will lose a lot of time and money with such projects, so I would recommend sticking with projects that have a more common subject. In the end, make sure to always have unique articles and to strictly follow the buyer's guidelines for any given project. If you do this, you'll find paid freelance writing both easy to come by, and easy to continue.
Regardless of whether you're looking to make a career out of writing for money or just looking to get paid for writing on the side as something extra, your options are endless. Just make sure you do some research on the person or company you've agreed to write for to ensure it's a legitimate offer and not someone who is going to take your writing and run.