The hiring process varies based on the type of role you are looking for.
Several park/resort roles (Merch, Attr, Cust, Foods, Front Desk, Concierge, Housekeeping, etc) are union roles. This means that when you submit your resume and go for your interview, it's essentially a pass/fail scenario. If you pass then you're placed on the wait list. As they work through the wait list it's first come first serve, meaning not the most qualified person gets it.
During the interview you can request information on roles currently open, and if you just want to get your foot in the door, it's easiest to take a role that has openings (even if it's not what you want) because after six months you can put in for a transfer. Union role transfers work off on seniority, not qualifications.
Then there are the Office and Technical / Salaried roles (Guest Relations, DPI, secretaries, managers, etc). These are filled based off of specific job openings/postings. These types of roles are not always open to outside people, internal candidates can view more opportunities. It's often recommended to start out in a role I mentioned above then try for the one you really want once you're in.
I've personally worked all over: Entertainment, Merchandise, Concierge... I've worked all 4 parks and just about half the resorts. I've been in union roles, O&T roles, and 2 different versions of salaried roles (exempt/non-exempt)... I'm pretty familiar with internal transferring so feel free to PM me if you have other questions. Oh, and I should mention, I did ALL of those roles in less than 4 years. I got my current role in summer 2011 and have stayed put.