At VUMC, experience/education and the like are important, but knowing someone on the inside is the key to getting hired. To do this, I decided to positon myself in a way so as to come into regular contact with VUMC employees. I went to work for a contracting company that handled the parking/valet services on the property. After many introductions and shaking hands, I would regularly mention my love of the medical field and experience in the medical materials management area. After getting a tip on an open position, I found out the Manager's name and emailed my resume directly to them. I have learned that with organizations like this, sometimes you have to circumvent the proper channels to gain an advantage on other applicants. Even if a supervisor/manager says you "have to go through HR first", getting your resume in their hands, or their Inbox may be enough to get them to call HR and have your application information forwarded directly to them for further review. Score!
I only had one interview, but obviously it was enough to get the job offered to me 3 days later. At VUMC, this is virtually unheard of. A month-long hiring process is the norm.
If you don't want to take or have the time to establish connections, be creative and look for ways to find a manager's name and email address. Sometimes, if you have their name, but not their email address, look for the addy of someone else that works there. Often this will give you an idea of how the manager's email address will look. If you send them your CV/Resume, and it gets returned to invalid email address, then mark that possible addy off your list and try another one. If you're using Microsoft Outlook, enable the Read Receipt option so that you'll get notified if they opened your email. Occasionally, someone will block Read Receipt Requests on their email (which means you won't be notified), but still take the chance they haven't enabled to block.
Be creative. Be persistent.
Good luck!