I accidentally logged out of Skype on my iPad, now I can't log in or find my password, and I was surprised to see that the Skype app does not have a way to help me.
The answer is that you have to go to your web browser and go to www.skype.com. This is the home site for Skype. Click on the login link. Then you will find the Lost Password link.
Fill in your details and you should be able to reset your password.