It is yet not possible to delete your account. You can only delete your profile information. See also https://support.skype.com/en/faq/FA142/How-do-I-delete-my-profile-or-Skype-Name
However, as some people told us: write an email to firstname.lastname@example.org (you'll find the adress for your country on the skype support website) and say, that you want to delete your account. If you're lucky, they respond within 48 hours. They might ask for some more personal information for verification purposes.
If you can't find any contact info and still wish to ask something, for example a question about what exactly is deleted, about data retention, etc., you may contact the domain owners using this info.
If you signed up for Skype using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Skype. Click the icon below to find out how.