While commonly associated with a nation taking military action against another, Imperialism can mean an assortment of things a nation does to dominate another without having to take direct military action. 

Diplomatically is the correct answer here. Diplomacy would allow the weaker nation some say in the process of what is happening. However, in the rest of these examples the stronger nation can simply force the weaker one to bend to its will. 

Though it began as a fight over Spanish control in the Caribbean, the Spanish-American War extended to the Pacific where American forces drove Spain out of the Philippines, effectively destroying the Spanish Empire. Originally intending to aid the Philippine fight for independence, the end result was American control of the island nation. 

With the spread of Western cultural and political influence many traditional territories were broken up by competing European powers. Most notably, the Berlin Conference broke up the African continent into arbitrary territories that ignored the local tribal boundaries and conflicts.

When a colonizer directly administers a colony it is called direct rule. This is because the colonial power takes over all systems of government for the colony.

When a colony is under indirect rule it means that the colonizing government has not taken over all aspects of the government of the colony. This means that the colony is free to make certain decisions without consulting the colonizing power.

Diamonds have become synonymous with Africa. The continent is rich with them, but they had not been discovered there until the mid-1800's, when a mine in South Africa found a large deposit of diamonds.

While there were many gold rushes in American history, there was never a truly large amount of gold in the United States. South Africa, however, is gifted with an abundance of it. This gold, along with the diamonds discovered 20 years earlier, made the British Empire incredibly wealthy, as South Africa was still part of the British Empire then.

When Britain invaded the Zulu Kingdom, they sparked the Anglo-Zulu War. The Zulu were able to win several victories early in the conflict, but thanks to their superior technology and numbers, the British eventually won the war. This British victory led to the annexation of the Zulu Kingdom into the South African Colony.

While the Zulu proved to be much fiercer opponents than originally thought, the British did eventually win. The Zulu won many early engagements thanks to their speed of movement and expert use of the terrain to ambush the British; however, the superior firepower of the British eventually led to victory in pitched battles.