Can one legally embed others YouTube video

Hi say I have a commercial site can I embed any YouTube video others for free or what is the procedure

Yes you can embed any youtube video others for free. IF video owner enables that embed option then it means you can use there video.
For embed you need just click on share button then click embed option.

From time to time you should check if the video is still visible on your site. The owner can disable the embed option any time.

Yes you can. If you run advertising on the page, you need to make sure you comply with the terms of the advertisers.

For instance, if you run Adsense and the whole site has thin content, save for the videos, it'll be the path to doom and Adsense ban.

The YouTube terms of service state:

"You also hereby grant each user of the Service a non-exclusive license to access your Content through the Service, and to use, reproduce, distribute, display and perform such Content as permitted through the functionality of the Service and under these Terms of Service."

This does become murky, however, if you are embedding content that should not be on YouTube in the first place like TV shows, movies and other similar content that breaks the YouTube copyright rules to begin with, you can run into copyright issues with the actual copyright holder. This is probably so rare it's unheard of, but for a commercial site I'd err on the side of caution. YouTube generally takes the full brunt of these takedowns and handles them quickly and since the embeds are branded, I'd imagine a rights holder would start with them anyway.

Of course embedding videos is free. As long as the video is public and the embedding option is enabled, you should have no trouble. I embed videos throughout my articles whenever I want to demonstrate something.

Yes you can, as long as you're sure the poster has the rights to post it in the first place.