In terms of defending, a counter attacking team will look to soak up the pressure before making a quick break towards goal. To replicate this in FM, you would use defensive instructions such as Drop Deeper & Stick To Positions. This keeps your players in a strong defensive shape.
In terms of attacking, it is all about that pace. While your opponents have plenty of players up the pitch to try break you down, you need to get as many forward as quickly as possible. (Much) Higher Tempo is suitable for this. In terms of other instructions, it is purely down to the preference of the manager as to how he wants his team passing the ball, where he wants to focus the pressure, etc.