Running a barony isn't all a matter of assigning personnel, taking advantage of opportunities and dealing with problems. Successful rulers are expected to build monuments to their nation's power and prosperity and having a functional purpose that benefits the peasants also helps.
Constructing Buildings (1/3): You may construct buildings to increase your barony stats. Each building has a cost in BP and a construction time. You may construct several buildsing simultaneously.
To start construction, select a building you need from the list on the right side of the screen and place it in an empty slot in the settlement.
Buildings: Special Bonuses (2/3): Buildings may provide special bonuses if you meet certain conditions (most commonly, two buildings must stand close together to grant the bonus). Make sure you use this feature to your full benefit when planning a settlement.
Some buildings can be placed only in designated spots or areas. As examples, a pier must be built on water and a mill must be built with no other buildings around it.
Buildings: Moving and Demolition (3/3): Demolish a building to get rid of it and recover half of the resources you spent on construction.
If you want to move a building, you will have to demolish the old one (gaining half the resoucres you spent on it) and construct it in the new desired slot for half the price. You won't have to spend any extra BP, but you will have to wait for construction to finish in the new location.
The currency of building is Building Points (BP), which are accrued on a weekly basis, although certain dialogue options, quests, events and projects can yield additional build points, and generally the more developed your economy is, the more Build Points you'll earn each week.
To check your kingdom's current stats, hover your cursor over the "Stats" bar at the top left of the screen. The categories that appear under the stats bar lists your kingdom's capabilities, resources and level of development in various categories. These can be improved by completing events and projects, but events are fickle, and a bad stroke of luck could just as easily lower these stats. The sure-fire way to improve them is by building cities, which requires time, Build Points, and planning.
To start building, click on the selected settlement's icon on the map to view its own personal contributions to your kingdom's stats on the left, and the buildings comprising the city on the right. Click the "Enter" button (the one on the screen, not on your keyboard!) to get a view of your city - or rather, what will soon be a city, as the case may be.
Note that there are buttons on both sides of the screen, with the left-hand buttons, "Stats" and "Built" providing identical information to what you saw on the previous screen. At the top of the screen some basic information is provided: - the name of the city, your BP, and the number of plots available. On the right side of the screen are more interesting buttons, "View" and "Build". View merely lets you look at the area without the clutter of the Build UI, so click on Build to get to work.
Clicking on the "Build" button will bring up a list of structures available for construction, as well as a grid representation of where you can build these structures. Each building requires Build Points to create, as well as time to construct, another task you should endeavor to take care of between bouts of adventuring. In return, constructed buildings provide various benefits to the city they're in, as represented by boosts to various kingdom stats. A Barracks will improve your Military might, a Shrine will increase your Divine rating, while Shops and Taverns will improve the Economy.
Note: Building multiple buildings of the same type in each settlement will get progressively more expensive. For example, the first Shop you build in an area will cost 20 BP, the second 30 BP and the third 45 BP.
This is all rather straightforward stuff, but to complicate matters, some buildings have greater effects when one is built next to another (an Adjacent Bonus) while others will benefit so long as another building is located anywhere within the same settlement (Coexist Bonus). These bonuses can only apply once per pairing, so building a Smithy flanked by two Shops will not do you any good.
Also, some buildings can only be built in specific spots, and are usually color-coded to make this simpler to plan out. Walls can only be built in green areas (at the boundary of your settlement), a Pier must be built adjacent to water (marked by a blue square), and Windmills and Watchtowers must be placed on isolated squares.
As a further complication, as you build up settlements they'll naturally get larger, for instance graduating from a village to a town. Larger settlements will allow for a more diverse selection of buildings to be constructed, and will also fortunately unlock more open building spots on your settlement grid.
Note: You can check the progress of kingdom events - including building progress - while exploring. To do so, when you're on the world map just click the castle icon on the lower right corner of the screen. Some events will require your physical presence, however, so it's a good idea to return regularly and not over-extend yourself.