Have you actually installed the Skype program? Signing in to your account via your browser won't work.
Download then run the full installer via this link:
When the install is complete, sign-in with your Skype name and password and you'll then be able to start using Skype's features.
I don't have a Menu Bar either. I believe it is because I am running Ver 2.8. Depending on what version will work with your MAC. I have to go to Skype at the topof your screen and click Preferences...
These are really opaque answers. I don't normally use a Mac, nor do I ever intend to, given how hard it appears to answer a basic question, but please explain how do you get to the menu on Skype for Mac. I want to change my password. How come this is simple on a Pc but impossible to explain in plain English for a Mac? Please just use regular English about what one needs to do. I always heard Macs were easier. But the Skype for Mac window shows absolutely nothing that would lead one to a menu.