Summarize:

Its app icon resembles an "S" inside of the Skype logo. This will open your Skype main page if you're already logged in. If you aren't logged into Skype, enter your email address and password before proceeding. It's in the upper-left side of the Skype window. A drop-down menu will appear. This option is in the drop-down menu. Doing so opens the Settings window. On Mac, this option will say "Application Settings" instead. You'll find this heading near the middle of the Settings window. On Mac, scroll down to the "Privacy" section instead. It's below the "Contacts" heading. Doing so will open a list of your blocked contacts. Scroll through the list of blocked users until you find the person whom you want to unblock. It's a blue link to the right of the contact's name. Doing this will immediately unblock the person and add them back to your chat list. This option is at the bottom of the window. Your contact should now be unblocked and available for chatting.
Open Skype. Click ⋯. Click Settings. Scroll down to the "Contacts" section. Click the Manage blocked contacts link. Find the user whom you want to unblock. Click Unblock. Click Done.