Answer: Daphne, there are a couple ways to do this. But first I have a question…do you have a WordPress.com site or are you self-hosted using WordPress.org? The are very similar, but they behave a little differently (there are more options with .org – including plugins).
I personally use Networked Blogs to publish directly from my blogsite (which is a .org) to my fan page. It’s not my favorite app, but it’s there and set up, so I use it. It can take a bit to get it to work properly as you need to be “verified” (either by users/friends or by adding a “widget” to your site).
They also don’t update to your page immediately. They have a schedule that they post by (let’s say it’s 4:00PM Eastern) so your post will go to your page then. Though, the higher your page ranks (site and/or blog), and the more frequently you update your blog, the quicker it could get shared to your Page. You can access the FB app here.
You could also use Publicize with his something that is available through WordPress directly (full disclosure: I’ve not tried this, but I do like the look of it). Here’s how to use Publicize for your personal profile and your business or fan page.
I’ve also seen folks with WordPress.com sites (usually those just starting out who don’t really know that there are other options out there), manually share their posts directly after it goes like using the social share (click here to share kinda buttons). It works fine and is really just a click away.
If you use a WordPress.org site, you can scour the Internetz for umpteen different plugins that will share your posts against any and/or all social networks. Just Google it.