We've had reports that the Skype app won't show up when searching the App Store by name. If you run into this, go to skype.com on the student's device and follow the links to the download page.
Skype is owned by Microsoft, and users will need to create a Microsoft account. This has been very problematic in the past because of Microsoft's limitation on the number of accounts that can be created in a 24-hour period from any single location (IP address.) If possible, have students create an account before class, and remind them to bring their log-in information. If Skype is being taught from lab computers, check for the latest version updates prior to class. Skype has been changing rapidly.
Also, for those teaching from Windows 8 computers, I would suggest teaching the desktop version and leaving the Metro version alone. The Metro (tiled) version lacks several of the desktop capabilities, and will be changing regularly until the next version of Windows (Windows 10) is released in 2015.
Skype takes a lot of bandwidth. Users will need to log on to your lab's Wi-Fi if bringing personal devices. Check ahead of time to make sure that adequate web speed can be attained for the expected number of students, or plan to use 2 devices as demonstration and practice devices.
Note: Download and install Skype, run and install updates, and test online with cameras and microphones before class.
Read blog posts about Skype