You’ll need to locate the place on the page that you’ll want the video to go and put your cursor there.
Pull up the video on YouTube and copy the URL for the video (i.e. http://www.youtube.com/watch?v=XXXXXX).
Go back into the WordPress page and click the filmstrip icon from the toolbar (should say “Insert /edit embedded media” if you hover your mouse cursor over it). Paste the YouTube video URL into the “File/URL” field. Check the “Constrain proportions” checkbox and change the width to about 500. Click the “Insert” button at the bottom to add the video to your page or post.
You can add text, pictures, etc. above or below the video, just be careful not to backspace or just delete it.