Yes, you can add more time to your opponent's game clock at any time except for tournament games. Follow the link at the bottom on the game-page. Set up the additional time you want to give your opponent below the Go board. You can add days to the main-time for all time-systems (Japanese/Canadian byo-yomi and Fischer time) and/or reset the byo-yomi periods (for Japanese/Canadian byo-yomi). Notes about added time is displayed in the game-info box on the game-page.
 
For tournament games, adding time by the players is not allowed, so that the tournament-director can limit the estimated amount of time that players will spend on the tournament-games. Some tournament director are allowed to add time to a tournament game on their own discretion.