If you use the latest version of Skype there is no need to back up your contacts as they are stored centrally on our server and can be accessed anywhere as long as you sign in with the same Skype Name and password.

Skype also stores chat histories and contacts locally. Skype for Mac OS X stores contact list files and call records in ~/Library/Application Support/Skype. You can back up all files and directories beneath it. To restore your contacts and data, simply copy the files back to the directory mentioned above.