You may have noticed that Skype does not have a button or any direct facility to log you out from all of your devices. As such, your contacts may see you as active and send you messages even if you have not logged in on the device in front of you. Then become upset on you for not being responsive :)
So, what is to be done in such case?
Some advised to change your password.
OK, this might be a solution, only that a lot of people claimed their remote sessions are still active and, on the other hand, maybe is not very convenient for you to change password every time you want just not to be seen on Skype.
So, thanks to the Skype community where this question was asked since 2013, here is the working solution, tested by me with a Windows 7 computer and with a remote session opened on an Android phone:
Step 1. Open a chat window in Skype with any of your contacts. Since you will text some commands which will not appear on your peer's, theoretically can be anybody. In practice, since you may do a typo or so, better avoid your boss's chat, just in case :)
Type:
/showplaces
This command will list all of your active Skype sessions (the one in front of you and any of the remote sessions as well). It will not be sent as a text message, but only return the result.
Make sure to avoid any space before the text. If you will see the command sent in the chat window, you have either a space or a typo somewhere.
The displayed result in my case was some mambo-jumbo out of which I can clearly see 2 sessions, one on the computer and the other on the Android phone:
You have 2 online endpoints:
{43436daf-0144-c222-b22c-efc345485637} ' computer name' (Windows Skype)
{4334cde3-b0e3-dea8-b0e3-4a3426a4b0e3} 'localhost' (Android Skype)
Now, to get rid of the remote sessions, proceed to
Step2. Type in the chat window:
/remotelogout
Now I can see live how my Android phone is being logged out.
A new /showplaces command will list either only the current desktop session, or together with a second one but marked with ():
{43436daf-0144-c222-b22c-efc345485637} 'computer name' (Windows Skype)
{4334cde3-b0e3-dea8-b0e3-4a3426a4b0e3} '' ()
And the final step is to logout your current session as well and ta-daa...
That's all, folks!