Write an informative, high quality article and submit it for distribution to other sites. At the end of the article, you include a tagline with a link to your website. Each site that publishes your article should also publish the link to your site.
Blog Comments
You can get some backlinks by commenting on various blogs. Just be sure that you do not spam; leave good useful comments. Also, if you want maximum SEO benefit from the comments, post on blogs that do not add the nofollow attribute to comment links.
Blog Posts
You can pay bloggers to post about your website, or you can offer them a free article in exchange for a link. Either way, go for quality blogs that do not post lots of ads.
Forum Links
Some forums allow you to add a link to your website in the signature - just be sure you do not spam the forums. Work to become a respected member of the community.
Buy Links
Google frowns upon bought links, but you can do a few, especially if you buy them direct from various webmasters instead of through a link broker.
Social Media
Many web 2.0 sites allow you to get links to your site. The key is to follow the guidelines and be a contributing member to the community. Spam is never OK, and it won't pay in the long run.