follow up on job applications

It seems like it is not enough to just apply for a job by filling out the application and submitting any requested information. How do I go about following up on an application? In some cases, I may be able to find the number for nurse recruitment or HR. What do I say when I am calling? How often do I call? How much is too much? There is one job in particular that I am really interested in. I got the email for the director of the department and sent her an email telling her that I applied online and would be interested in speaking with her further. Not even sure if she has any say over the hiring. I did not get a reply. Do I email again? What is appropiate and who do I contact? Is phone contact better than email? Any help would be appreciated. Thanks!