Skype for Windows, Mac, Linux, and Skype for Windows 10 (version 14), Andriod (6.0+), iPhone and iPad.

1. Tap or click your profile picture. 
2. At the top, select Sign out. 
3. Choose whether you want Skype to remember your account and app preferences on this device, for example your selected theme.
   • Yes: Sign out without deleting your username, password or app preferences.
   • No: Deletes your username, password and app preferences on this device. 
   • Cancel: Stay signed into Skype.

Skype for Web

1. Click your profile picture.
2. At the top, select Sign out.
3. In the confirmation window, click Sign out again.

Android 4.0.4 - 5.1

1. Tap the menu  button. 
2. Tap Sign out.