Contact other sites and ask them to link to yours. Write articles and submit them to article directories. It takes a lot of work to build quality backlinks.
google count backlinks but show less backlinks in google. for details of your links check with yahoo or google webmaster tools.
for a simple thing....you can doing by visiting other blog and comment to their article.... if you had more of money you can offering the webmaster to buying a link from them to place your link to their blog...(for this way you must check their blog PR)
as people have suggested you have to start your link building campaign in which you need to mix up different activities... like social bookmarking , article submission, Rss sharing and submission and more related activities in social network in which you can get direct readers from blog....
By using Link Building , you can increase your Back links for Google In Link building, you can do: Bookmarking, Directory Submissions, Article Submissions, Forum Posting, Blog comments etc.
It will better for you if you will submit your blog in blog directories and Social Bookmarking Sites.Regular new blog posting is necessary.
Submit your blog to blog directories, submit rss feed in feed directories, update your blog regularly, comment on other blogs that helps to increase backlinks.
You could put your website in your signature that way people get an idea what your blog is all about, then maybe some might approach you with a good link exchange offer
link exchange, directory submissions(especially dmoz), social bookmarking, creating valuable content, sponsoring tools, etc
Write quality articles with relevant keywords and don't hesitate to link other blogs/websites. When you have a bit of experience, you can start contacting people who run a blog/website on the same topic (even if you're writing on a very specific topic like what to feed to horses or how to win the diversity lottery, you'll always find someone who has a similar website). Directories can work pretty well too but don't submit too many links/day.