I can give more insight into relations between the two than the actual war effort.
Canadian Prime Minister Louis St. Laurent and his Secretary of State for External Affairs Lester B. Person were well on their way towards guiding Canada as a "middle power" within the world and stepping out of the British commonwealth. At this time, Canada began becoming what Norman Hillmer and J.L Granatstein refer to as an umpire on the world stage. Peacekeeping and working with U.N. mandated missions became the priority for Canada in foreign affairs such as the Korean War and the Suez Crisis. Canada became one of the key "choirboys at the concert of nations." Canada was not compelled to go into missions with the United States that were not backed by the U.N. (much like their stance in the Second Iraq war)
Relations were not always at a peak however, as Canada decline L.B.J. for troop support. Prime Minister Pearson also criticized the war effort while speaking at a university, which and was asked to meet with L.B.J. immediately after with him replying "Don't you come into my living room and piss on my rug." However, Canada was also playing a vital role in NORAD, and the Russian threat was much more imminent than the threat than the N.Vietnamese. Canada remained allies by fighting containing the "Northern Front."
Canada also provided many raw materials, weapons and other goods that were shipped to the US and then was sent to S.Vietnam. Someone else will have to provide more insight into what Canada contributed to the war effort.
Source: "Empire to Umpire" Norman Hillmer and J.L. Granastein
Fun Fact: Norman Hillmer did his graduate studies at Carleton University under none other than Prof. Lester B. Pearson. I then did my thesis with Prof. Norman Hillmer. Meet J.L. Granastien and he seemed like a dick!
Canada supplied “millions of dollars of humanitarian aid to South Vietnam” (but not North Vietnam) and allowed the United States to use Canadian military bases “as a testing ground for Agent Orange and carpet-bombing runs.”
Chantal Allan, Bomb Canada: The Case for War and Other Unkind Remarks in the American Media, (Athabasca University Press, 2009), 46.
One of the seven suppliers of Agent Orange, Uniroyal Ltd., produced “about 2.6 million litres of the herbicide sprayed on the jungles and people of Vietnam” from Elmira, Ontario.
“Vietnam War: Investigating Agent Orange claims,” CBC Digital Archives, November 8, 2012, http://www.cbc.ca/archives/categories/war-conflict/vietnam-war/canadas-secret-war-vietnam/agent-orange.html
Canadian companies filled “American defense contracts for shipments to Vietnam,” the contents of which included “cartridges, guided missile components, demolition material, bulk explosives, aircraft engines, sonar equipment, and personal armor.” These contracts accounted for “almost 3 million of the fiscal ‘74 period” and were clearly designated by the United States “specifically as support for operations in Southeast Asia.” Furthermore, companies bidding for contracts with the U.S. government were provided with forms which indicated “where the material is to go, so the company at that juncture is perfectly aware…of where that particular item is to be sent.”
One contracted Canadian company wrote to the Department of Industry, Trade and Commerce, asking what it should do if it received information that “the destination was in an area against Canadian law.” The written response was, “in essence…let us know, and we’ll proceed to find a way around it."
“Supplying the war machine,” CBC Digital Archives, June 7, 2012, http://www.cbc.ca/archives/categories/war-conflict/vietnam-war/canadas-secret-war-vietnam/supplying-the-war-machine.html
Canada accepted “an estimated 50,000 to 125,000 Americans” escaping the draft, and Canadians held many large protests that added to a growing international anti-war solidarity. Canada also accepted Vietnamese refugees who fled their homeland. At the same time, 30,000 Canadians voluntarily joined the United States’ military to fight in Southeast Asia during the Vietnam War.
Edit: The CBC links have changed since I last used them and no longer lead directly to the source article.