Access the Startup from the Task Manager in Windows 8 to keep Skype from starting up on its own whenever you power on.

The Task Manager is a pretty good thing to have pinned to the task bar. You may find it by picking Search from the right navigation that has Search, Share, Start, Devices, and Settings in it. Then search for "Task Manager" and when you find the Task Manager, pin it to the task bar. If you launch the Task Manager, you will see a tab for "Startup" and going there will show you a list of what spins up automatically upon starting up. Right-click on Skype and pick "Disable" from the menu which appears to keep it from automatically starting.