In the case that you want to change the (primary) email address associated to your Skype account, follow the below procedure:
- Connect to Skype: http://www.skype.com/en/
- Click on your username to access the profile page:
- Scroll to "Account details" > "Profile".
- In the page that opens scroll to "Contact details".
- Click on the Edit button:
- From there you can edit your primary email: