The states were Jerusalem (corresponding to today's Israel); Tripoli (today's western Lebanon); Antioch (in the western border area between Turkey and Syria); and Edessa (in today's eastern Turkey).
These four states were all subject to the Roman Catholic Pope. The strongest between them were the Kingdom of Jerusalem. At no point did any of them appear as independent states from the other ones, and they were never freed from their original European influence and connection. There were conflicts between them, but these had background more in personal interests than the interests of the states themselves.
The organization of the states were complex, and closely related to feudalistic structures.
One step down in the hierarchy from the ruler, was the institution known as Court of Lieges. It was a strong and long-surviving structure; put together by fief-holders, vassals and under-vassals. It had total control over legislative matters, and decided over important issues like ownership rights. The court's power was so strong that it even decided over matters of succession to the throne. But despite this theoretical control, the Court of Lieges were in many instances controlled by certain people or groups.
Below the Court of Lieges, were the Court of the Burgesses, which had jurisdiction over individual citizens.
But it was more complex, as the church's representatives exercised much power over large parts of the Christian states. Four metropolitan sees were subject to the Patriarch of Jerusalem: Tyre, Caesarea, Bessan and Petra. Moreover, the Catholic church exercised its power through seven suffragans sees and many abbeys. The Christian institutions didn't lose power, as they were the beneficiaries of donations of properties in both the Middle East as well as in Europe. The church did of course develop into becoming the richest power all in the states, even if the official leaders were from normal secular royal families in Europe.
The rulers were however rich, profiting from custom taxes in the ports, tolls claimed from the caravans passing from the Syria/Mesopotamia and further to Egypt and North Africa.
The main challenge of the rulers were not to defy the church institutions, but make sure that they kept sufficient troops to protect their territories and allowed them to make advances into Muslim-ruled territory (often with substantial Christian populations) when this was considered appropriate. The solution for this problem, proved to be one of the longest living fruits of the crusader period: the establishment of religious orders of knighthood. These brought in revenues in the same manner as the church institutions, but the members were soldiers. The knight orders grew strong also from its ability to draw members among the younger sons of feudal houses.
The economy of the Christian states proved to be good, as they served as ports for imports from new territories to the rest of Europe. The income of the rulers, orders and the church did little good for the normal inhabitant, whether it be Europeans or natives. But the high trade activity provided for higher living standards than what was common in most of Europe. Most of the merchant activity was in the hands of the Italians, not surprising since Italian ports had the best combination of connections to the rest of Europe and sea routes to the Middle East.