Dan,
I've been a student in the CEC delayed entry program (DEP) since November, so I may be able to help you out a bit.
The application process can be long and tedious. If I remember correctly, it involves filling out an application, doing an online security application, sending in your transcripts, and meeting with your advisor to fill out the Navy's degree completion plan (just a list of every class you need to take to graduate and when you will take it). You also do have an in-person interview with an officer (I can't remember if it is before or after the paperwork). This interview isn't really anything to be worried about. It was surprisingly informal and laid back. They want to know why you think you would make a good officer and such.
Once this is all done, you wait to hear what they have to say (can take up to a month, I think).
If they do select you, you have to schedule a time to meet with your ascessions officer and they swear you in. Do this ASAP, since your pay starts from the date you swear in.
One other tidbit for you: I was told that the CEC program is lumped in with the BDCP, therefore you may be able to get in the program at 3 years from graduation. It may be harder to get accepted at this point in your academic carreer, however, it is worth a shot. Worst case scenario is that they don't accept you, and you re-apply at 2 years from graduation.
The process is long, but worth it. The biggest part that slowed my process down was my own ambition to fill out everything during a busy school year.
Good luck to you.
-Dan P.