There are two ways to build links through blogging:
1. Create your own blog
2. Post to other people's blogs
Creating your own blog
There are many companies that can get you set up with your own blog.
The one we used is Wordpress. We created a free blog, soapnuts.wordpress.com. There are also options that cost money and will get you your own domain name without the .wordpress.com. We recently upgraded to the paid domain name of soapnutslaundry.com for around $10 for the year. Blogs move up in the google rankings based on links and having current information. As you distribute your free articles, make sure they have a link to both your blog and your website. That way, they are building the rankings of both. After you distribute the free articles, make sure you post them on your blog. That way, you are adding content regularly to your blog. The search engines will see this and adjust your rankings accordingly. Also make sure to link to all the pages on your main website. In the eyes of the search engines, your blog is a seperate site linking to and voting for your main website.
Posting on other people's blogs
Another, much more time consuming method of blogging to build links is posting on other people's blogs. Once you have a Wordpress account, you will have an id that you can use to post on other blogs that accept it. The best blogs to post on, though, are the ones that you can give your name and url. Where it asks for your name, put keywords that you want to rank in for your website. When I first started zealously blogging on other people's blogs, I noticed that my site kept moving up in the rankings for "Matt Johnson". That was because I was putting my name, rather than keywords for my website. I corrected that, lost the Matt Johnson rankings & started gaining in the keywords I was looking for.