First, create a custom web page. While viewing the custom page on your Site, select the "Customize Design" button. Next, add the YouTube content block from the Video section of the Content tab by dragging and dropping it onto your page.
The Edit menu for the content block allows you to title your video, insert the YouTube link for your video, and tweak the video's appearance and layout on your page.
You can add as many YouTube blocks to a page as you'd like, control their width and arrangement, and also control the theme and design on that page.