Action Details
Requirements and how-to articles for LinkedIn's action:

You can share videos with your network.

You need this to get it done:

The video you wish to share.
File format: .asf/.flv/.mpeg-1/.mpeg-4/.mkv/.webm/.h264/.avc/.mp4/.vp8/.vp9/.wmv2/.wmv3
Maximum file size: 5GB
Minimum file size: 75KB
Maximum video duration: 10 minutes
Minimum video duration: 3 seconds
Resolution range: 256 x 144 pixels to 4096 x 2304 pixels
Aspect ratio: 1:2.4 - 2.4:1
Frame rates: 10 fps - 60 fps
Bit rates: 192 kbps - 30 Mbps
Note than unlike with photos, you can only share one video at a time in a post.
The content of your post (maximum of 1,300 characters.)
Posting Location
If you are an admin for a company page(s) you can choose whether to post from your personal profile or from a company page.
You can choose who your post is visible to - Anyone, Connections only or Group members. You can also choose whether to enable or disable comments on your post.
Hashtags (optional)
You can add hashtags to your post in order to help it get discovered by other users. However, be careful not to add too many (the optimum number is generally believed to be between 3 and 5) as it could risk looking like a spam post.
Captions (optional, but recommended)
Adding captions to your video makes it more accessible. Captions must be uploaded in the .srt file format.
Video Thumbnail (optional)
You can add a thumbnail image for your video.
Requirements missing or found errors? Report

How-To Articles
A list of useful links for you:

Posting and Sharing Content - Overview | LinkedIn Help
How to write a post and share it with fellow LinkedIn users.
Sharing Photos or Videos | LinkedIn Help
Information about sharing photos and videos.
Video Sharing Troubleshooting Guide | LinkedIn Help
File requirements and troubleshooting for video sharing.
Link missing here or found errors? Improve How-Tos