How did colonialism give rise to the Vietnam War?
Colonialism helped to give rise to the Vietnam War because it made the Vietnamese hate the French and want to overthrow them. The fact that the main resistance to the French was done by the Vietminh gave that group (and its leader, Ho Chi Minh) credibility among the Vietnamese people even after the French left and the Americans came to support an independent South Vietnam.
In the mid to late 1800s, France gradually came to own all of what was called French Indochina (including Vietnam, Laos, and Cambodia). The French colonial regime was fairly oppressive and exploitative -- this was not a situation where the French were trying to help modernize Vietnam so as to turn it over to its natives later on. Instead, the French were simply using Vietnam for their own benefit.
Naturally, this made the Vietnamese very unhappy. They wanted to rule themselves, and anyone who stood up against the French looked good to them. The Vietminh's desire for freedom led to the conflict with the French after WWII. This conflict is what led to US involvement in Vietnam.