When you have established a series of blogs that establishes you as an authority on a topic it is time to distribute your content on other sites. Guest blogging is an ideal way to share your content and get links back to your site!
Kiss Metrics has a great report on the ultimate guide to guest blogging that is worth a flick through.
To post as a guest on someone else's site you need to approach them and show them the value you will add. Searching via social media or google for sites or other authority leaders in your space is a good way to find potential sites to guest post.
Introducing your expertise to a new audience is a no-brainer but be aware, often content owners want "fresh content" and not content that has been repurposed from your blog.
Check out the site's traffic through Alexa.com. Search for the blog on social media sites and see who is talking about it and how many fans and followers they currently have.