After you have played a game you get the opportunity to vote for your PotM. Simply go to the game page and you will see a vote button next to each of the players on the attendance list.

You can vote for more than one player, but when you vote for more than one, your vote is then divided.
48 hours after the game has been played, the results will be published with the player who has won the PotM award

You will be able to check your PotM record through your profile page as well, with the number of total awards next to your profile picture