After you've uploaded the video and it's available to everyone, click the Video Manager
button near the top of the window or below the video box.
This will list all of your videos. Click the Edit
pull-down menu next to the video you want to alter.
Then go to the Privacy Settings
pull-down menu and select an option:
The default. Anyone can find and see it.
The video won't appear on any Internet searches, nor will YouTube add a link to it on any page. In other words, there's no way for anyone to get to it unless you give them the URL.
Only people you invite will be able to watch the video. You can invite up to 50 people--but only people with a YouTube or Google account.