Once you get what a niche is, finding become a bit easy. The following tips would help you.
Your area of expertize
What is your area of expertise. May be that can become your niche in which you provide solutions or entertain audience.
Let's say you are a Maths teacher, you can start a website about teaching Maths to students, passing on valuable lessons and tips.
Your Interest and Hobbies
Find the topics you like to work on as hobby or the areas that interest you. When you work on something that your hobby too, there is nothing like it. Ideas flow naturally and you become more productive as you want to do more.
Let's say you like to do gardening on weekends, that is your hobby and you love to do it. You can start a blog about sharing your experience as how to do that from sowing the seeds to harvest.
Find a Problem to Solve
Try to find problem that you or other people face on day to day basis but don't find or know a good way to solve it.
Let's say you have an IPhone and buy & download applications. The cost of the application changes would it be nice to know when the cost goes down for applications and notifies interested people, helping them to save money.
Depending on your team size, you can choose work on single aspect or multiple aspects of the problem. However its highly recommended to start with one aspect and then as you see growth add more. Mostly people start on thier own, and remain the only person, so narrow down your niche scope.
Determine Niche Class
So see what you niche falls under, based on that decide if you can create that many content pieces to keep up with the demand.
You need to look for factor inorder to maximize your profits or returns. All niches are not profitable or equally profitable, some are 10 times more than other and so on.
For example, the Real Estate niche can provide 3 to 5 times of profits compared to a Entertainment niche with the same number of pageviews.
See : Top Profitable Niches
Review market saturation around that niche.
Try to find how many companies/groups/people have blogs or website. Are they trying to solve the same problem that you want to solve? If yes how do you distinguish from them? Basically lesser the market saturation the better are your chances to come on the top.
Find latest trends and hot topics
Find out what is every body talking or is into these days. Even better the areas which are just starting to pick up. Since there is nothing much about that area and if you can research about it and provide a value there you would be much better in next year or so when this area peaks.
For example, IPhone apps market is hot these days, or Google Android is getting hot, so you can be the market leader in that space if you start right now.