Click on the Share link located underneath the title of the YouTube video.
If you just want a persistent link, click on COPY next to the URL and paste into Blackboard as a web link. Note that you can choose a starting time by checking the Start at box.
If you want to embed the video, so students see a viewing window right in Blackboard, click on the Embed link.
The next window that pops up includes the embed code to copy and paste into Blackboard.