If you want to publish your WordPress blog posts automatically to Facebook page or other social media sites like Twitter, Google+ and others then there are two plugins which I would like to recommend, they are very easy to setup and works smoothly.
1) Jetpack by WordPress.com
Jetpack is a bundle of various useful plugin developed by team of WordPress, it has over 12 million users and it is regularly updated. One of its feature is Publicize which may help you to publish your blog post to Facebook page or your timeline.
Goto Plugins>Add new> Search for Jetpack by WordPress.com> Install>Activate Plugin.
Connect to wordpress.com
If you have wordpress.com account then sign or create new account.
Sign in with your wordpress.com account to authorize.
Goto Jetpack (On left sidebar)> settings>Scroll down>Click Publicize and click it>click configure.
Connect your Site to your Facebook Page
On the Sharing page, click the Connect button next to the Facebook logo. A message will appear asking you to authorize the connection between your WordPress.com blog and your Facebook account. It’ll ask three times for providing access 1) to public profile and friend list, 2) to post publicly on your behalf and lastly 3) to manage your pages, Click okay every time.
You’ll then see a success message and dialog box. You can choose if you would like to publicize to your profile or one of your pages. Once added your page, later you can add more pages by clicking Add New button.
Please note that for connecting to pages: You may need to use a Facebook account that has admin rights to the Page.
Test Post – Successful
2) NextScripts: Social Networks Auto-Poster (SNAP)
If you like to publish your blog post to more social sites than what Jetpack provides then you may like this plugin, It allows you auto posting to variety of social websites such as Facebook, Twitter, Google+(Google Plus), Blogger, Tumblr, Flickr, LiveJournal, Flipboard, FriendFeed, DreamWidth, Delicious, Diigo, Instapaper, Stumbleupon, LinkedIn, Pinterest, Plurk, VKontakte(VK.com), YouTube, App.net, Scoop.It, WordPress, etc. The whole process is completely automated.
Your new post will be published to all your configured social networks. You can reach the most audience and tell all your friends, readers and followers about your new post. It works with profiles, business pages, community pages, groups, etc.
Click NextScripts > in menu bar click Products> You can download either Free or Pro version.
In your blog dashboard, Go to Plugins>Add New>Click Upload Plugin>Choose files>Install Now>Activate Plugin
Go to Settings (in left sidebar)> Click SNAP>Add New Account
For every social site there is link for Detailed Facebook Installation/Configuration Instructions, you can visit this link before going further to understand how you can configure particular feature.
Posting to Social Sites
Once it is configured, when you write new post you’ll find various options for posting it as the end of post box.