At the moment, I simply take an ID, which is simple enough to obtain by looking a the video details or the URL
My experience with users and this case, is mostly in phpbb where to add a youtube video you insert the Video ID like so:
It is so bad that there are 2 or 3 different threads explaining how to find the ID and properly embed youtube videos.
Consider what you are asking:
Copy/Paste full Url:
Select Url + Ctrl/Command C + Ctrl Command V And you are done, some folks might right click instead, but I believe this is a widely used operation that might already be internalized and almost a reflex by virtue of use.
Parse the Instructions given since they are novel. Parse visually where the ID starts and ends, and then Select Id + Ctrl/Command C + Ctrl Command V.
Again, this is a specific case vs what most people seem to do, copy/paste the full url.
Are there other alternatives that I might not be considering?
You could be more explicit with a placeholder showing the ID format and instructions on where to find it, but unless the ID is central to your UX, you might be asking the user to do something a RegEx might easily do.