If you have knowledge of the subject you plan to write about then you may be able to write an entire article without utilizing any other references.

If you do not possess that in-depth knowledge of the subject then Google is your friend.
You don't need a Masters degree in the particular subject you are writing about; just a general knowledge of the subject matter and some time spent researching the topic.
Spend some time on the internet doing research, just be careful not to steal anyone else's work and call it your own.

Writing articles gives you a sense of accomplishment. Seeing your article in print or published to so many websites gives you a sense of satisfaction of having accomplished something useful, which others may find informative as well.
Also, for creating traffic and exposure to your website, writing articles is a very effective means of promotion.

For example, if you have a website about dogs, then write an article related to that subject. The article should contain useful information, or you can write about some of your own personal experiences.
Then just add your site links in the body of the article, or in the Authors resource box.

Whatever you decide to write about just be sure to do a little research and write something that will be interesting and informative for the reader.
You will then be seen as somewhat of an expert in the subject matter, even if you may not necessarily be.

After you have written your article then you will want to submit it to your favorite article sites or blogs. You may submit the article to as many sources as you are inclined to.
For maximum exposure the article may also be submitted to many social bookmarking sites such as Digg, Technorati, and many others.
You may also utilize the services of a publishing agent if you decide to try and get the article in print.

If you are writing the article purely for fun then you may only wish to submit it to a few places. On the other hand if you are using this article as a method for creating traffic for your website, then you will want to submit it to as many sources as possible.

Whatever your motives are, writing articles can be a rewarding and enjoyable experience.