You can fine players for red cards, skipping training and poor performance and, to my knowledge, no other reason.
Skipping training - You will get a popup email in your inbox telling you a player skipped training. You have the option to fine him in the bottom right.
Suspension - If a player gets suspended, you will get an email reminder and the option to fine will be in the bottom right. Don't fine the player unless it is at least a 2 game suspension, as 1 game suspension fines will anger the player and all his friends due to the new dynamics feature.
Poor performance - I'm not sure of the minimum average rating for you to fine a player, but if you know a player is not up to standards the option will be there when you right click a player's name.