You can adopt the the 3 following ways to increase backlinks to your blog:
1. Manually: You can submit you blog to various directories or websites to increase backlinks.
Naturally- If your blog content is interesting, informative and resourceful, other webmasters will link to your blog. This will raise the number of backlinks to your blog. Other than this, you can create content which is meant to spead virally, leveraging blogs with the aim of garnering manifold links in short time.
3. By entering into partnership with other bloggers: You can ask other webmasters to post your blog in their blogroll. You can also request them to put a link to your blog. This will help you to get backlinks.
Regards
Monalisa