To use skype first you need to register, which you have already done. Then login with your user name and password. Once you have signed in you have 2 ways of calling, one is by simply dialing a number the same as an ordinary phone, the rates are very cheap have a look for yourself. http://www.skype.com/intl/en-gb/prices/callrates/
The other way is by adding another persons accout name to your list of contacts and calling them from your computer direct to their computer, this way it is totaly free, you don't pay anything. A skype phone is a good thing to have, I have one myself, it makes things a lot easier and the built in mic and camera you have on your laptop will work fine.
The money you have paid will have been added to your account, it's a bit like topping up your mobile phone, this is your SKYPE CREDIT and will decrease as you make calls to mobile phones or land lines.
If you are having problems loggin in to your skype account check your email. I'm sure that they must have sent you your login details via email, you could also try the forgoten password page here.https://secure.skype.com/store/member/login.html?message=login_required
I have logged a call with their support team but there is no telephone number at all to contact them
I don't think they have a telephone number that you can call but I have found this link which might help you - some topics on how to use skype and a contact customer support page, you can fill it in and send them a report.http://support.skype.com/?_a=tickets&_m=submit
Hope this helps you!