I would expect the questions to be no different than a regular interview, and I would prepare for it in the same manner. Dress professionally, have your documents with you, smile, be confident, etc. As for the environment- limit/eliminate distractions and background noise. Ideally you should be alone in the house, or shut in a room with explicit instructions to not be disturbed. Leave your cell phone in another room. No tv, radio, or noisy appliances in the background. Sit in a straight-backed chair and make sure there is plenty of natural light and no glare on the screen or your face. If you wear glasses, elect for contacts or go without them for the interview, since the reflection on eye glasses is very distracting during Skype and prevents the interviewers from seeing your eyes. Use the largest screen computer that you have and look at the camera, not at the screen. This will give the interviewers the impression that you are making eye contact, where looking at the faces on the screen makes it appear that you are looking down or to the side, depending on the location of your webcam.
Since this interview is for a BSN-DNP program, expect questions about your past education and experience, why you wish to pursue your DNP, your future career goals, your work ethic, and teamwork abilities.
Other advice, from someone who has interviewed and been interviewed on Skype:
Take a really good, hard look at what's behind your chair. Once I had the embarrassing experience of being interviewed on Skype for a video YouTube piece and when I got to preview it for editing I saw my cat having a nice, thorough bath on the shelf behind me! (They didn't notice, but I called it to their attention, we all had a good laugh, and they blurred her out before it went up.)
Remove all clutter from behind you, including the stuff over the back of your chair. All of it. Move your computer to a place with a neutral background if you can't. Close the door so you won't have any noisy surprises. (Once I was on a conference call, thankfully with no video, and a cat chased a chipmunk right across my desk and down the other side. Havoc ensued. Thank god for mute buttons.)
Dress as professionally as you would if you were sitting in the HR office. Small earrings (if you're female), no bling, suit jacket.
Turn down the light in your screen as much as possible if you wear glasses, because the glare on the lenses will be blinding on the other end. If you don't wear glasses, check ahead to see what light level makes you look your best, not washed out or green or orange!
Set the little window that shows your face to you as close as possible to the camera, so when you look at yourself it looks like you are attending to the person on the other end.
Practice with a buddy ahead so you can get a critique of your presentation and appearance.
If you have to wear earbuds to hear better, go with the smallest possible earbuds, buy some black ones, and put the wire behind your head so it's not a distraction to the viewers. The idea is to make it like a regular conversation, and how much do you like trying to talk to someone with headphones on? Would you wear headphones to a face-to-face interview? No, I didn't think so. Visual cues are even more important in a screen interview.
I have never given this much thought before until I saw your replies. I definitely will take these advice to heart. I have a toddler so these advises help.
If you have a toddler, GET A BABYSITTER. Either recruit family/friends to help, or pay for a sitter. Do not even think that you can do this interview during nap time because I can guarantee you it would be the one day that even the most predictable and clockwork of toddlers will decide that he/she doesn't want to nap. Mark my words.
So if your toddler is going to be home on interview day, spring for a babysitter to either get your toddler out of the house during the interview time (preferred) or to entertain said toddler in another part of the house far away from you and the computer.