When the tourney's started click on tornuments and scroll down to the 'in progress' ones and click 'watch'
How to watch live Tournament

Thank you, finns! However, I cannot find this option. Maybe this is because I have only free account?

Elensar, you should see the "tournaments" tab located next to your "new game" tab. Click that, then do as finns recommended.In the list of tournaments, those which are progressing should have "watch" next to them. Click it then a new tab should open with a sub tab named "games" click that to view one of the games that are in progress.

Thank you Kansha!
Could you or anybody else tell me how the System assigns the color of pieces to each player in a given (not tournament!) game. I've played three games one after another and had black pieces in all of those three games. Just wondering what it depends on.
Thank you in advance!

Probably random. Random number generator with 2 numbers. 1 is white the other is black.
Thank you finns! I also don't think player has any option to explicitly set up the preferred color for his/her pieces.

Do you have time for this?
Sorry, I didn't quite get your question. Time for what?
I'd like to watch live tournament games as they progress. How can I do it without joining (playing) in tournament?
Thank you.