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.