Earning a gold medal any of the combat missions requires you to earn a set time, accuracy and headshots. Once you start a combat mission make sure your shots count and aim for the head. Use your Dead Eye ability as much as possible to increase your chances of a perfect shot.
You can keep track of your mission progress by pressing and selecting stats. You will then find a sub-menu called missions. Here you can see all your badges for each missions, you will also be able to select any mission and replay it.
Most missions are fairly easy once you know what to do. You will either get this from natural progression or by replaying a mission you know really well. Always skip cut-scenes as they add to your mission time. Try replaying the missions "Cowards Die Many Times", "Lucky In Love" and any of the Home missions.
You will be accounted for accuracy, time and headshots within the missions. Try not to miss headshots as this will ruin your final score.