I've installed EzVid and it appears to be kind of buggy. I managed to record the screen only to find out that no button exists on the main interface. However, if you click the question mark next to its name, you'll see a list with hotkeys that you can trigger. One of them (actually CTRL + U) will render the current job to a local file and then attempt to upload it to the YouTube.
While it might be faster this way, use the old-fashioned way to save the video locally and then visit Youtube to upload the video. This will also give you additional options to customize various parameters.