Scattered around the country you sill see light blue house icons with a green exclamation icon nearby. This shows the settlement is currently occupied by the government, and in need of liberation. This set of achievements depends on the liberation of the provinces, not the settlement. Some provinces only have 1 settlement, some have 3 or so. Liberate all needed settlements to free the province. By pressing and going to the political map, you can see how close to liberation the province is by seeing how full the green bar is.
In order to begin your liberation go to the green marker to see your guerrilla contact. He will be a happy looking gentleman waving at you surrounded by large amounts of ammunition. Go up to him and press to begin the liberation of the settlement.
There will be two different types of ways to liberate a settlement, depending on the size of the settlement you are liberating. Smaller rural towns and government bases will all follow the same pattern. First eliminate enemy soldiers. After a sufficient amount have been eliminated, you will be directed to destroy the enemy barricade, which will be shown on your map by the red marker. This can be destroyed by a single rocket, or by two grenades. After the first barricade is eliminated, continue to kill troops until prompted to destroy the second barricade. The same pattern continues until all 3 barricades have been destroyed. Once the third falls, you will be prompted to take down the enemy flag. Walk up to the flag, and press to switch flags, and this will complete the liberation as a victory for the rebels. As you progress through the liberation, you will see a bar on your screen with green on one side to blue on the other. This bar shows the progress of your liberation. As you get closer to green, your victory becomes closer.
The second type of liberation only occurs in larger urban cities. There you will have just an open war against government troops. In this type of conflict, the progress bar will be very important, because it will be your only means of knowing how you are doing. As soon as the progress bar is all the way to the green side, you will be prompted to switch flags. Follow the red marker on you map, and press to claim your victory.