In order to dominate the map, you’ll need buildings and armies. To construct buildings, simply select the province you want to build in and select the Construction option. From there, you can select the building of your choice - but keep in mind that certain buildings have requirements that must be met first. Some, for example, will only become available after a certain number of days have passed.
Similarly, units can be recruited via the Production option in the province menu. Units require a specific building - varying between unit types - to be constructed in the province before they become available, and certain specialist units may require multiple different structures.
All units and buildings have an upfront resource cost, which is required to begin the project. Although all of the resources will be reserved when the project starts, they will be consumed slowly, over time, so cancelling a project early will recoup more resources than cancelling it closer to completion. In addition, units and buildings have an upkeep cost, so they will cost a small amount of resources every day that they are on the map. Buildings can be disabled, which deactivates their effects in exchange for removing the upkeep cost, while units will consume resources for upkeep until they are destroyed.