1. Shoot video (smartphone quality is acceptable)
2. Upload video to YouTube via smartphone or computer
3. Once the video is uploaded, click "Share Link" to access the embed code
4. Click Embed, then choose the checkbox to "use old embed code"
You must select to use the old embed code in your eBay auction description. The new embed code uses <IFRAME> which is prohibited in an eBay item description.
Visit my auction listing for an example of an eBay item description that includes a video clip: