So you want to know how to get backlinks? The most obvious way is to ask for them from authority sites in your niche. But before you do, there are several things to consider.
First of all, what do you have to offer? Why should they give you the link? Do you contribute to the niche with unique and interesting content? Or do you offer the same content in a new way? There are many ways to crate value but you have to make sure you crate it before asking for links.
Then you have to be considerate about how you approach with the request. Be polite and give them a reason to link to you. Perhaps you can donate some great content, or your website would compliment their content well? Find ways to be valuable to them and make your proposition.