If you want to have a look at Skype you can download the software here <
http://www.skype.com/...-_-16123210-_-1558696 > assuming you're using Windows, but other operating systems can be chosen to suit. As hc4361 says, you don't need a webcam, but using one does add an extra dimension to the conversation and you can include more than one person in the frame. (you would also need a spare USB port) If you and the person in the room were just using sound with no picture then it may be difficult for the listener to determine who was actually speaking at the time.
Skype to Skype connection is free, but if you just want to make a telephone call, you would need to buy credit from Skype, using the normal methods one would use to purchase anything on the internet. I've never had to. Good luck with what ever you choose to do.