There's no need to back up your contact list. With Skype, your contacts are stored centrally on our servers. You can access them anywhere, as long as you sign in with the same account and password in Skype. However, if you wish, you can still back up your contact list:
- Sign in to Skype.
- In the menu bar, click Contacts > Advanced > Backup Contacts to File…
- Choose a destination to save the file to, and click Save.