Skype for Windows, Mac, Linux, Skype for Windows 10 (version 15), Android (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 application 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.