Your city depends on peasants to function properly. Peasants produce and defend for the city, in return you must feed and find them jobs.
Peasant immigration depends on free land available and the living conditions in your city. Exploring new lands will bring in new peasants looking for a new and better life. Once the city runs out of space, peasants will stop coming till new lands are explored. Exploring land can become quite expensive, as new lands are mapped prepared for living and roads built to allow full access to your province. As your lands increase in size it is more difficult to find new areas so it becomes more expensive. It is wise to explore land in blocks of 50 acres or more as this is less expensive in the long run.
Peasants can be assigned to jobs in the population screen. Not all the jobs are shown from the start, some jobs require that special building be built. Each job has a skill rating which represent how good your peasants are at their job. This skill ranges from 2.5 to 10. A skill 10 worker produces 4 times more than a 2.5 skilled worker. Every time you add workers to a job type, the skill is reduced as it averages out amongst the old workers with skill and the new workers coming in with no skill. So it is a good idea not to change workers around too much so that their skill will rise to high levels.
The entry level of a worker is 2.5, this is the minimum it can fall to. If you build a university the skill will rise, as new workers will already come with knowledge of the job in question. If you own a university the entry level rises to a minimum of 5. This effectively doubles all production, so a university is extremely important to have.
As your population increases your unemployed levels will rise and you will have to assign workers to jobs. It is sometimes a good idea to have some unemployed workers ready to take on the jobs of any of the current workers who may die. So if you get a negative peasant amount these are deducted from the unemployed and not from the workers. This stops you from having to fill in jobs every turn your population number drops. When the population drops, the negative amount of peasants is deducted from the unemployed pool automatically. If your unemployment pool falls to 0, then workers are removed from the jobs directly.
Once your population grows above 1000, you will have to think about building medical centers. These centers keep control of your population's health. If you health score falls too low, then you stand a chance of a plague or illness breaking out. You must have a proportional number of medical centers to your population count. It is also wise to add a few more than is required in case there are any emergencies or events that may cause your health to drop below the norm. It is common for other kingdom to poison or try to spread infections amongst enemy province, so keep an eye out and be prepared with plenty of medical back up. If a plague breaks out, a lot of peasants may die which is definitely an unwanted situation.
Another important score to keep an eye out for, is the morale. Morale shows how contented your population is. This is usually related to their social conditions and tax. If you charge too much tax the people will grow discontent. To raise morale you can build pubs or hire entertainers. Entertainers will only be available once the theater plans are complete. It is always a good idea to have good morale in your city and plenty of pubs and entertainers to dissolve any dissention. It is common for enemy kingdoms to spread discord and lies to your people through evil propaganda, so make sure you have good morale raising capabilities. If morale drops too low, your kingdom may revolt. If this is the case, you will lose control of your subjects and the population and construction screen amongst others will be unavailable to you. It is recommended that you lower your tax to 0 or 1 as soon as possible so that morale rises. If your morale is not to far gone and low, then you can probably take a few turns with 0 tax and wait for it to rise.A revolt will stop automatically if your morale rises above 85 points.
If the revolt is of a more serious nature and your morale has fallen too low, then it would be a good idea to declare martial law. This can be done by hitting the MARTIAL LAW button on the TAX page. If you declare martial law, your army will patrol the streets and control your population. This stops any revolt, but comes with a price. During martial law, your army may not attack and will defend at half their full strength. You may stop martial law at any time by pressing the same button in the tax screen, but make sure that your morale has risen enough or your population might fall back into revolt.
Generally, your population is easy to control once you get a hang of the main factors influencing it. At worst, peasants can be quite forgiving and there will always be new immigrants to fill the ranks of any who leave or die, as long as there is decent living space in your city.