There are two types of Skype Accounts.
If you sign into Skype using your username - that username is typically what we would call your "Skype ID."
However, if you sign into Skype using an email - then you signed up for Skype using your Microsoft account. This is the account you use for Microsoft Products. (Windows, XBox, etc.) This means that your account ID is your Live ID, ie. Live:italki_320941. However, this ID is not shown on your Skype Profile - all that will show up is your email.
To find your Skype ID on a Mac, simply go to File > View Profile:
To find your Skype ID on Windows, simply select your profile picture, and your Skype name will be displayed in your profile.
For users that sign in with their Microsoft Account, they will not be able to find their Skype ID there, but the email address of their Microsoft Account instead. This acts in place of their Skype ID. We recommend that users use Skype Accounts that have a Skype ID because an email address can be linked to multiple Skype Accounts, while Skype IDs are Unique.