How are nationalism and imperialism related?

Nationalism is related to imperialism because it is a tool of imperialist governments that helps them to rally support for their cause among members of the empire. Nationalism refers to a feeling of devotion to the state held by the people who live there; imperialism refers to the desires and actions of the government of a nation to assimilate territory. In most cases, in order for a government to wage a successful imperialist campaign, it must first induce the population that it already rules over to have strong feelings of nationalism, which can then be played upon to help citizens to justify the imperialist mission. For instance, nationalism (the love of one's own nation) can be easily manipulated into outright xenophobia (the fear of those from outside the nation) with the right propaganda campaign. This relationship can be observed repeatedly in history.

Nationalism doesn't necessarily entail imperialism, but throughout the course of history, the two ideologies have often enjoyed an intimate relationship. When it first arrived on the European scene, nationalism was seen as an emancipatory ideology, one that would free nations from the tyranny of foreign empires, allowing them to assert their cultural and linguistic identities.
The growing confidence that this inspired, however, often turned into a desire for territorial expansion whereby newly-liberated nations became the oppressors. Take the example of Revolutionary France. The founding of the French nation and its corresponding overthrow of the monarchy was supposed to inspire other nations in Europe to throw off the shackles of monarchical oppression. But as the crowned heads of Europe waged war on Revolutionary France, the revolutionary regime began to impose itself on neighboring countries for both strategic and political reasons. This was both a defensive measure and also, on the face of it, a gesture of solidarity with fellow oppressed nations.
The problem was, however, that many of these nations found it hard to tell the difference between liberation and oppression. Many of them welcomed the French Revolutionary Army overthrowing old and corrupt monarchies, but they didn't appreciate the French running their affairs and effectively establishing an empire on the backs of what were supposed to be free, liberated nations.

Nationalism and imperialism are often related. Nationalism refers to pride in one’s country. Imperialism is the desire to gain land beyond one’s borders.
 When countries become imperialistic, one factor that often is involved is the desire to spread their way of life. Imperialistic countries believe the way they do things is superior to the way other countries or the people in other countries do things. Thus, the imperialistic country feels it is its duty to help the less fortunate people and the less fortunate countries in the world by showing them the ways to do various things. This includes how to set up a government and an economic system and how to live their life.
The British and French established colonies for many reasons. One reason why they expanded into Africa, Asia, and the Americas was to show the people who lived in these areas how to improve their life by following British and French ways of doing things. The Germans believed they were superior to the people in any other country. Thus, they felt they could do what they wanted to do when it came to controlling and conquering other places. Imperialism and nationalism often go together.