Run Skype. Under people, select / highlight the contact you want to remove >> Right Click >> Click Remove.
Did you select the contact?
Ok so I dont think they quite explain it well. Here's what you do. In skype, scroll over to your contacts. Click on the contact as if you were to start a conversation. Then, anywhere on the screen, right click once. At the very bottom right corner of your screen will be 3 buttons. The one in the very corner will show a skype person symbol with an X and will say "remove" beneath it. Click on this, and it will ask you "are you sure?" That's all there is to it. I wish helpers in forums were more in-depth and lengthy with their answers