If a game is postponed and the new date falls outside of the duration of the contest you are in, the points will not be counted. The salary for the game(s) is immediately returned to your balance.
If your contest ends on a Monday and a game is postponed to the Tuesday after, you will not receive points for the Tuesday games. Only games played within the contest's duration will count towards your score.
If you have an active contest happening and a game is postponed or rescheduled to a date within that active contest, it could be treated like an added game as usual and you might need to choose whether to activate or bench the player's game via a toggle on the Schedule view. Also, added games default to benched.
For more details on activating and benching players in Tournament contests see: Activating and Benching Players
For details about postponed/rescheduled games in Head-2-Head contests see: Rescheduled and Postponed Games' Points