You will start by downloading Skype. Next, create an account and log in, and then search for your friends on Skype. After you have added them, you can chat for free. You don't really need a camera unless you want to video chat.
Yes you do need a camera on the computer for Skype to work. To call someone's cell phone from Skype you need Skype credits but just to video call you don't. You can only Skype your contacts on Skype. To Skype one of them click on contacts then their name and then hit video call.