The usual way is to add them to friends and then you see that in the "Friends" tab on https://chess.com/live I think.
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How do I view another player's live game on chess.com ?
According to this spport article: https://support.chess.com/article/789-how-can-i-watch-a-game and this forum post: https://www.chess.com/forum/view/help-support/how-do-i-see-my-opponent-s-current-games
I should be able to see the games from their profile. However all I get is "No games in progress" (unless they also have correspondence games in which case it shows those games and not the live game), and their "Last Online" status says "In Live" . I can't figure out how to actually see the game in progress.