While you could search for people through Facebook, many people won't add you unless they already know you. That makes getting an introduction with a hiring manager very difficult via Facebook alone. That's why there are add-ins for Facebook such as BranchOut.
BranchOut is a new service available through Facebook that lets you build professional connections with your current friends. Think of it as LinkedIn for Facebook.
You just add the company you currently work for to your Facebook profile and then invite others to do the same. They fill out their company information and invite their friends. Eventually you can search your extended network for connections to companies for which you would like to work. Then you can ask for the direct connection.