It's a piece of cake to display a YouTube video using Sakai's Lessons tool, using the "Add Multimedia" button. In the Add Multimedia URL box, type the web address of a YouTube video, click Save, and presto, your video displays.
What about Vimeo videos? Since Vimeo is not YouTube, if you want to display a Vimeo video (versus displaying a link to a video), you have to find the embed code to display it. And not just any embed code will do-it has to be "old embed code". It's not hard-you just have to know what to do before copying the Vimeo embed code.
Once you have the correct Vimeo embed code, you can use the Lessons "Add Text" button, and the Text Editor Source button, to display the HTML area, where you can paste your Vimeo embed code. Need details? Here are the step-by-step instructions for displaying Vimeo videos in Sakai.