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.
Publicly visible text/images often aren't properly deleted even when you succeed in deleting an account. Try editing or deleting them manually before deleting the account itself. If you're unsure what happens to your tracks you can always contact Skype and ask personally. By the way, deletion requests don't necessarily mean your data will actually be deleted (e.g. due to legal obligations).
Si no puede encontrar ninguna información de contacto y todavía desea hacer algo (por ejemplo, una pregunta acerca de lo que se elimina, sobre la retención de datos, etc.,), usted puede contactar a los propietarios de dominio utilizando esta información.
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.