i had my first skype interview this application season. my best advice is to PRACTICE! not just what you say, but what you're wearing, what's behind you, and so on. my mom gave me recommendations about how certain colors looked on her computer and stuff like that. my interview wasn't long (about 20 minutes) and the professors were very nice. also practice because i found looking directly at the camera rather than at the faces onscreen difficult to get the hang of. i used a wireless connection and didn't have any problems, but if yours isn't quite stable you'll want an ethernet cord.
one more thing: if you live in a house with other people (as i do), graciously ask that they refrain from showering/partying/cooking or talking loudly during the interview. while i was practicing with my mom someone started to take a shower, and she said it sounded very loud on her end. i'm glad that happened so i could ask people not to do that during the real interview.