There currently is no mechanism that allows you to automatically follow a player from board to board. However, you can add players to your Following List which can be used to filter the Players and Live Games Lists so you can more easily find your friends to challenge or watch.
To add a player to your Following List:
Select the Players tab. Browse or search the players list for the player you would like to add. Tap/click on the player's avatar, then select the Follow button.
To filter the Players List:
Select the Players tab. Tap/click the Filter option at the right. Tick the box for Following, then select the Done button.
To filter the Live Games List:
First, select the Watch Games option from the main menu at the left. Then use the Sort By Game pull down to select Following.