Well if you are using Skype probably not much. Any Core 2 or up should do the job and probably a fast single core if it is backed by a reasonable amount of RAM. You need a good internet connection though. 1 MB a second upload will do the job well. Anything under that and you may find you lag.
It depends of the resolution of the video you are going to deliver, the compression for the video /the softuer you are using/... The video component usually needs much more bandwidth as the audio. But maybe the most important is how many sides will participate in your conference, how many streams. And please - what software you will use?