How To stop Skype from starting automatically

To stop Skype from starting when you turn on your computer: click on Tools -> Options -> General Settings and un-check "Start Skype when I start Windows."  Click Save at the bottom right corner of that screen.

Next, sign out of Skype.  When you re-start Skype, un-check the "Sign Me In When Skype Starts" underneath where you input your password.

That should do it.