Short Answer 
The three main strategies for a prince to maintain control over a newly acquired state with a history of freedom include ruining the state to establish authority, residing within the state to build trust and loyalty, and creating a loyal oligarchy to govern on his behalf. Each method carries its own benefits and risks, with the oligarchy approach often providing a smoother transition of power.
Step 1: Ruin the State
The first option involves completely bringing the state to ruin, which can lead to chaos and disorder. By destroying the existing structures and systems, the prince can establish his own authority. However, this method is highly destructive and can result in backlash from the former rulers and citizens.
Step 2: Reside in the State
The second approach is for the prince to actually live within the newly acquired state. By immersing himself in the daily life of the citizens, he can build trust and establish a personal connection with the populace. This hands-on approach helps to foster loyalty, but it requires significant commitment and can expose the prince to various risks.
Step 3: Create a Loyal Oligarchy
The third and easiest method is to establish an oligarchy that is loyal to the prince. This entails appointing a small group of trusted individuals who can govern on his behalf. By allowing them to maintain some degree of autonomy, the prince can secure their loyalty while keeping the state stable. This method often results in a smoother transition of power and minimizes resistance from the people.