If you are blogging then you must have created Facebook Page for your blog. Now do not keep it blank, post something so that Facebook users who have Liked your Page can engage with it. You can post status updates with interesting discussions or can update it with your newly created blog posts.
If you want to share your blog posts on your Facebook Page then the best way is do it manually, that is, copy the link of your article and add it where you write your status update. This will add a thumbnail image (if you had added any image to your post) and a small summary of the post to the status. However, it is always recommended to add Open Graph protocol to solve some of the problems and remain Facebook friendly.
It is always best if you do it manually but in case you find it time consuming to login to Facebook and update the status of your Page whenever you write a new blog post then you need a third-party application that will import your blog feeds to your Facebook Page automatically. There are many applications available provided by sites like HootSuite, dlvr.it, Blog RSS Feed Reader, etc.
The the first two sites are packed with features but HootSuite is great (even for the free plan) as it has covered most of the social networking sites including Google+ and Twitter but to use all of the features you have to pay a price. If you want a simple and free application then go with RSS Graffiti, found on Facebook.
But again, after reading the article “Facebook Fail – Mashable”, I still recommends you to do it manually.
P.S. This post has been updated.