In your Skype profile (Skype -> Profile -> Edit Profile), you need to have no year selected. This basically means that when you are selecting your birth year you want it to be the blank field at the very top of the drop down list.
Skype will not let you select this directly, so if you click the uppermost year (from memory it is 1900) and then press the up arrow on your keyboard it will select the blank field.
When done correctly, the profile will look like this:
Edit to expand answer:
It is also possible to edit your profile through the Skype Website.
Sign into the site (same password as what you use to log into the application) and under "Account Details" choose "Profile".
Hit the Edit button, make your changes and click save (why doesn't the Application have this?"
Log back into the app and your changes should be reflected there.