Medals are earned through doing just about anything. Killing an enemy with a physical attack for example. Medals can be earned through Campaign, Agent Hunt, and Mercenaries. There are a total of 264 different medals in the game, and you need to earn 150 of them. You should be able to unlock this after spending some time in every mode, and without too much extra effort.
At the end of a chapter, and at the end of a game of Agent Hunt/Mercenaries, it will list all your medals you earned in that game. In Agent Hunt, make sure you finish the game to receive credit for your medals. In Mercenaries, if you die or quit before the timer reaches zero, you will not receive credit for any medals that might have been earned during that game.
You should have a good head start with around 100-120 medals after completing all the campaigns. After that, play in the Mercenaries and Agent Hunt modes for 1-2 hours each to earn some easy medals and surpass 150.
If you have just a few left and are looking for some easy medals earn, or if you're just curious, you can find a list of medals in this thread HERE.
You can keep track of the number of unique medals you've earned by viewing the "Decorated" titles under titles in the Dog Tags menu. Add the 3 numbers for your total number of medals.