Long tail keywords get much less traffic than more general keywords but they are often high-converting and can draw quality traffic to your website. In fact, in some cases long tail keywords draw more traffic than general keywords. Below are some simple (and free) methods for finding long tail keywords.
Check Google's Autocomplete Suggestions
When you type a broad search term in Google it will display a drop-down list of suggestions for completing the search phrase. Because these suggestions are based on search volume this is still one of the best ways to see which long-tail keywords are ranking for a particular niche keyword.
Check the “People Also Ask” Boxes on Google Search Results
When Google shows you the results of a search it includes a 'People Also Ask' box that shows related queries. This is easy way to find long-tail keywords related to the one you are looking for and can give you some good ideas about other ways people phrase search queries related to your seed keyword. Another bonus is you can click on the sites listed to get more ideas.
Use Google Trends
Google Trends is a great keyword search tool and one of my favorites. It shows you how search interest has changed over a period of time (that you can specify) and also shows you a Related Queries box that can be useful for finding other long-tail keywords related to the keyword you've entered. Note that most of the keywords listed in this box are less well known keywords that most other keyword research tools won't find. It can also help you work out whether interest is waning or booming for your niche and keyword.
Use Question and Answer Sites Like Quora
Quora is a question and answers sites where people answer other people's questions on a wide range of subjects. By looking at the answers you can see what problems people are trying to solve related to your keyword. It also shows the most popular questions which can help you focus your search to long-tail keywords that are related to those questions. There are other similar sites out there, such as Yahoo! Answers, that you can check as well.