If you ever wish to obtain power, fame, or fortune, you must understand the basics of expanding your province and building your infrastructure. While war is always an option for growth, in many instances, you will need to peacefully expand your province. Below, I will describe the methods and benefits of each of your options.
Your People
First off, you will need people to make your province a success. Without them, you have nothing. It will be important, however, to find an effective balance within your population. The total number of people within yours lands is limited by space, and that total includes both peasants and military forces. Because only the peasantry raises families, you will need a large peasantry if you want to continue replenishing your population -- and that means a small military. If you military is too small, however, you are in danger of attack from outside. It will be up to you to come up with an adequate balance, but that may often be dictated by what your neighbors are doing as well.
Economics: Employment, Taxes, & Utilization
Utopia features a rich, vibrant economic system. The buildings on your land employ people to generate tax revenues for your province. In addition, your people power your buildings to provide non-financial benefits to your land.

The currency of choice in Utopia is the gold coin, demoninated by either "gc" or "$", the dollar sign as you know it. Your coffers need be plentiful if you wish to grow your province over the long term. You have one primary source of money, and that is tax revenues. It will be important to ensure that your people have adequate work: all buildings except housing will employ 20 men or women.

With too much housing and too little work, many of your peasants will be unemployed and provide little or no tax revenues. However, with too many commercial buildings and too few peasants, your buildings cannot function at capacity either. A farm cannot grow food without farmers. A Hospital cannot save lives without doctors. Each building (except Homes) on your land will require 20 men or women to provide their full benefits. This is measured in Utopia by Utilization. The fewer peasants per building, the lower your Utilization, and the less benefits your lands provide - however, all buildings automatically provide 50% of their benefits, regardless of your labor situation. With volunteer labor, your buildings can actually achieve utilization beyond their theoretical capacity.

Exploration
To gain additional lands for your province, you must send an exploration team to search out and claim your new territory. These expeditions will require both money and soldiers. Unfortunately, as your empire grows larger and receives more notoriety, fewer of your men will be willing to go on these dangerous excursions. Once you have your new lands in place, you will be able to begin developing them into more useful territory. It is important to understand that your people are essential to exploration, as they settle the lands. Your people will not allow you to explore unless at least 50% of your land has already been put to use.
Construction
Land alone is nice to have, but without buildings and infrastructure, it is of little use to anyone. You have a variety of buildings to choose to build, but remember this: You will need many people to make your province go, and you will need to provide these men with jobs to work. Only employed peasants will bring in the tax revenues that make your province go!
Your Construction Options
Homes While all land houses some peasants, setting aside acreage specifically for the purpose of housing can help to increase your total population. All provinces should set aside a portion of your land for residential areas.
Mines Because mining is a fairly stable and self-sufficient operation, Mines provide you with a small but steady source of income. Mines provide a source of income above and beyond standard tax revenues.
Farms Food is vital to the growth of any and every province. Without it, your peasants and military will starve! It is important that you keep an adequate portion of your land as farms, or you will find your province quickly fall to ruins.
Mills Mills are all about building better buildings. Your mills make the building process much more efficient and help you to construct buildings more cheaply.
Armouries Armouries give your men better facilities with which to train themselves into a stronger fighting force. Over long run, this allows to you build better troops at lower costs.
Barracks Barracks help train your troops and keep them in better shape. In combat, this allows your men to conduct battle more quickly and return home more hastily.
Strongholds Another source of training and development, Strongholds provide a locale from which your men can learn the most advanced in combat techniques, giving them a unique edge in combat when attacking other provinces.
Guard Stations By providing centralized areas to regroup and conduct battle, Guard Stations help to strengthen your defensive capabilities and ensure that your men have every advantage possible defending your lands.
Banks By creating a central place for monetary transactions, you can increase the overall efficiency of your economy. Banks help boost overall income -- and thus taxes collection -- in your society, while also protecting your gold from would-be looters.
Hospitals Hospitals are a valuable way to keep your military in good health. Oftentimes in battle, you will find many of your soldiers wounded, but not killed. Without Hospitals, these men will often perish without treatment. With them, your men may be saved.
Guilds Alas, Wizards are needed to cast your spells, and Wizards can only be trained at these Guilds. Developing a powerful army of Wizards takes time and patience, as well as many of these Guilds.
Towers Your Towers serve as a locale for your wizards and mages to work to develop runes. They allow you to produce new runes each day, giving you the ability to cast spells.
Watchtowers Watchtowers serve as watchposts for potential problems within your lands, mostly caused by thieves. Having an array of Watchtowers can help protect your land from infiltration.
Schools Schools are vital to making your peasantry smarter and poised for studies in the intellectual arts. Having Schools helps give your people the fundamentals needed to advance in the sciences.
Universities The ultimate locale for students, your Universities will help provide them the resources they need to learn the arts and sciences that will give your province an edge in the future.
Stables Stables help breed, train and house War Horses which can be used by your military to strength your offense. More can be learned about War Horses within Chapter III, "Going To War".
The Actual Numbers
The term "%" below refers to the percentage of land you have of that kind of building. For example, if you have 10% of your buildings as Barracks, "% * 2" would refer to 20%.
Homes Houses 30 People
(Non-Homes House 15 People)
Mines Earns $30 Per Day
Farms Produces 60 Bushels Per Day
Mills Decrease Building Costs by % * 4 (60% Max)
Armouries Decrease Military Training Costs by % * 2 (40% Max)
Barracks Lowers Attack Time by % * 2.5 (50% Max)
Strongholds Increase Offensive Strength by % * 2 (60% Max)
Guard Stations Increase Defense by % * 2 (60% Max)
Banks Increase Income by % * 1.5 (No Max)
Protect % * 4 Gold from Thievery (60% Max)
Hospitals Decrease Combat Losses by % * 4 (60% Max)
Guilds 1% Chance of Training a Wizard Daily
Towers Produces 10 Runes Per Day
Watchtowers % * 3 Chance of Catching Enemy Thieves (30% Max)
Lower Thief Training Costs by % * 2 (40% Max)
Schools Increase Science Effectiveness by % * 2 (60% Max)
Universities Decrease Learning Costs by % * 4 (60% Max)
Stables Produces One Horse Per Day
(Max 100 Horses Per Stable)