Recruitment Office
Recruitment offices train infantry over time for a small fee of 250£ per day.

Recruitment offices are a very cheap building, both to construct and to run. Since their cost to construct as well as operate them is minimal, you should usually fill up every province you own with them. They will recruit infantry in that province over time, and thus are essential for building up your military.

Barracks
Barracks train infantry over time more rapidly than recruiting offices, for 1000 grain and 500£ per day.

Barracks are a more elite form of Recruitment Offices, but they come with a price - their 1000 grain consumption per day (40/h) can make them inaccessible for many nations. However, there is little advantage to having your grain production significantly above 0 (unless you want to trade it), so you may want to put up a few barracks even with some of the more food-starved nations.

Double-resource provinces also produce twice as many men in the same amount of time, so putting barracks there is generally ideal.

Upgrading the Barracks to level 2 will double the consumption and train bonus (from 50% bonus to 100% bonus). However, beware—at 1/4 or 1/2 completion, a "Level 2" barracks will cost the full 2000 grain/1000£ per day but only boost production of infantry by 75%, so leaving incomplete level 2 barracks is not a very good idea.

Fortress
Fortresses protect your men garrisoned within them.

Fortresses seem irrelevant at first glance, but are essential for your survival in most games. Early game, when only infantry are fielded, a fortress can make a huge difference (even at level 1) in combat and thus potentially save you an outright defeat - make sure to build a few defending key provinces, even if you are a little short on iron.

Later game, their defensive advantage becomes more to house rail guns and stall your enemy's artillery fire, but they can still be useful. Level 2, 3, 4, and 5 fortresses hide units within them, and thus fortresses placed in key locations can prevent your enemy from gaining valuable information about your nation's army.

Harbour
Harbours decrease embarking and disembarking time at their location, as well as increasing resource production in their province by 25%.

Harbours are one of the more luxurious buildings in the game, and are out of the question for some nations near the start of the game. While some nations have an excess of wood (such as Sweden and Spain) and should consider building a few harbours near the beginning, many others (such as Morocco) may want to save their wood for other vital and less expensive buildings. The main advantage of harbours lies in the fact that they are free to operate once constructed.

However, the disembark advantage they give is by far their most minor benefit. While you should be sure to place them in the correct location so as to speed up movement along that route, it is more important to put them on provinces with resources you desperately need (for example, on Sweden's coal or grain) for their valuable 25% resource production boost. Finally, keep in mind that you need them (along with a level 3 or 4 factory) to produce Battleships in that province!

Railway
Railways increase move speed by 250% and resource production by 33% in their province at the cost of 500 coal per day.

Railways are perhaps one of the most misleading buildings. Their 250% move speed bonus can often mean the difference between a victory and a defeat, and thus there are often a few provinces in which a railway is essential for your country to excel. However, like Harbours, their main advantage lies in their resource production boost (33%), and use this wisely, especially since coal is often a valuable resource to many nations and thus their periodic cost of 500 coal/day cannot be taken lightly.

Try not to overbuild railways unless you know you can afford the coal, as otherwise you will find that you have wasted a good deal of money and have to leave them deactivated. However, if you can maintain their effect, they can be invaluable for their move speed advantage, their production advantage, and finally their accommodation of railguns.

Factory
Factories allow you to construct heavy weapons, as well as slightly increasing resource production in their province.

Factories are essential to any nation's survival past the first few weeks of gameplay. Producing Artillery, Tanks, Railguns, and Battleships (to date), any modernized army will need them to support their infantry and assist in assaulting coastlines, fortified positions, or other armies composed of such advanced technology. Even if you don't want the more expensive units, it can be advantageous to upgrade your factory anyways - not only does it give you about 8% more resource production in the province per level (topping at 33% at level 4), but it reduces the production time of all units available, meaning that artillery take 4 days to produce from a level 1 factory and 1 day from a level 4, while Tanks take 3 days to produce from a level 2 factory and only 1.5 to produce from a level 4. As such, you should usually focus on getting a few level 4 factories rather than a lot of level 1 factories.

Capital
The capital is the central hub of your empire and increases the morale of your provinces based on how far away they are.

Capitals are the least used and perhaps least appreciated building, as they are rarely lost (except in total defeat) and only one is necessary. However, their morale advantage can be key for the survival of the nation - provinces gain morale based on their travel distance to the capital. Additionally, morale can start to drop quickly if no capital exists.

You should usually leave your capital where it is, except if it feels threatened or, more likely, when your empire grows primarily in one direction. It is generally a good idea to keep your capital towards the centre of your empire, as the morale boost will pay off the cost relatively quickly and keep your people happier as long as your empire lasts. While a capital change may seem minor and expensive, it can make all the difference between a stable empire and a weak one.