Hello! You can use Skype without a credit card...calls to other Skype users are always free. Skype does offer certain paid services which would require a credit card -- calling "real" phone numbers or creating a phone number which is tied to your Skype account are examples -- but these are optional services.
Also, be sure you're downloading the official Skype client from this website:
I hope that helps! Please let me know if you have any additional questions.