Watch, Replay and Learn
For anybody who wishes to improve their chess but doesn't want to upgrade to a premium membership the best way to see some of the best moves is to look into the Games or Player tabs beside the Challenges tab. There you can find one or three minute bullet games that involve Grand Masters and Chess Champions. If you watch their games it is then possible to replay the game move by move at your own pace and then present yourself with an analysis of what moves players are doing, why they're doing them and most importantly when they are doing them.
As they are moving their pieces at an average of one move per second don't be surprised if you feel dizzy watching them.