How to send a video privately in Facebook

You can send a video in Facebook to a specific person only via Home → News Feed

Enter your news feed message for the person – example: “This is my video”

Attach your video file. After entering your text message inside the box, click on the video Icon below the box.
Choose between Record a Video, or Upload a Video, depending if you will record a video now on your webcam (connected to your PC, or built-in your laptop) or you already have a file in your computer.

Follow the prompts.

Record a small video, small meaning a record time maximum of 30 seconds.

Choose the specific person to send the video to. Click on the Padlock icon beside the Share button.

Choose the last option – Customize.

Choose Specific People in the Make this visible to section. Type the name of the person in the space provided.

Click on the Save Setting button.

Lastly, Click on Share button to send your news feed video to the person .

How to hide photos and videos you are tagged in from the rest of the (Facebook) world

As of today, these settings in Facebook still applies:

Go to Account - Privacy Settings.
Under the section Sharing on Facebook, click on the Customize Settings link.
Scroll down to the section Things other share.
On the setting Photos and videos I'm tagged in, click on the options and choose Custom.
The Custom Privacy pop-up appears.  Change the Make this visible to setting to Only Me.