One method would be to simply write about what interests you. Throw a few articles out there on a given topic and see which topics, or niches, perform well for you.
Another method would be Google searches. Trying searching Google for some keywords that you are familiar with. You can find "underserved markets," another favorite writer term, by doing searches and seeing which keyword phrases don't yield a lot of good results. Doing research often yields niche markets on accident. If you don't find a keyword phrase yields good results, why not write some of your own?
Here are some personal examples of niche markets that I have found that do well for me:
- Loom Knitting
- Freelance Writing
- Canning and Preserving food
- Raw food recipes
- Parenting Children with Special Needs
- Herbal Remedies
A word of caution on the first method. Don't be fooled into thinking that just because a niche doesn't perform well on one writing website, that it won't perform well on another. A good example would be the websites Suite101 and Squidoo. These require two very different styles of writing. Suite101 has authoritative articles that are edited and require sources to be cited. I consider the writing there the be scholarly work. Squidoo on the other hand has no editor and sources are never cited. I have some loom knitting articles on Suite101, but they don't look their best there because pictures aren't allowed throughout the article. They show up at the bottom. There also aren't a lot of sources to cite when writing knitting patterns. Writing knitting articles at Suite101 doesn't work very well. At Squidoo, it works wonderfully. The pictures can be placed anywhere I want them to better show the steps to the reader. My herbal remedy articles I save for Suite101. Nobody wants to trust a natural remedy article that hasn't been edited and has no sources cited. You get the picture.
Hope that's helped you brainstorm a little for some ideas on your own niches. Get out there and Google some keyword phrases. Once you found a few, write about them. See which articles perform well and which ones don't at that site. Once you've found a niche that works for you, keep at it! You can read more about niche marketing here.