There are many reasons to respond with a “not much” answer to the question in the title of this post. The Nation’s John Nichols acknowledges some of them in his article “Justin Trudeau Just Showed American Democrats How to Win the Next Election“:

It is certainly true that Canada’s political process is distinguished by traditions, structural characteristics, and nuances of party history and personality that make the country’s elections very different from those in the United States. Despite the increasingly “presidential” character of Canadian campaigns, voters choose parties rather than presidential candidates (and party leaders sometimes lose in their own constituencies and end up not just out of the running but out of Parliament). Canadians have more political options than Americans: Liberals, Conservatives, and the NDP run provincial governments; the Greens and the Bloc Québécois sit in parliament. Canada has shorter campaigns that are dramatically less expensive. Canada has a different media system, with stronger commitments to public broadcasting, serious debate, analysis, and dialogue. And, of course, while Canadian Liberals were campaigning to turn out a Conservative prime minister, American Democrats will be campaigning to carry on from a Democratic president while at the same time ending Republican control of Congress.

However, anytime there is an upset national election in North America it makes sense for Democrats to search for clues, and Nichols offers a few potentially useful observations, including:

The 43-year-old leader of Canada’s Liberal Party was not supposed to come out of the country’s 2015 election as its prime minister. At the start of the race, Conservative Prime Minister Stephen Harper, ally of George W. Bush, role model for Scott Walker, was locked in serious competition with a cautiously left-leaning New Democratic Party. The traditionally centrist Liberals (at their best “vital center,” at their worst blandly managerial), having been very nearly obliterated in the previous election, did not look particularly viable. And party leader Trudeau was frequently dismissed as the good-looking but inexperienced son of a great 20th-century prime minister.
“Seen at the beginning of the campaign as the least ready for the election of the three main party leaders,” observed the Toronto Star at the end of the campaign, “Trudeau managed in 11 weeks to shape a compelling political narrative and provide Canadians with a credible alternative to Harper and the NDP’s Thomas Mulcair.”

As for the “how” of Trudeau’s upset, Nichols writes,

Trudeau surprised almost everyone by running a campaign that veered left on economics–so much so that analysts noted that, on several critical measures, the Liberals outflanked the historically social-democratic NDP…He declared that his priorities would be job creation and policies to benefit the middle class. And he said he would invest in the future, rather than cheating it with austerity cuts.
Trudeau proposed to tax the rich in order to fund programs for everyone else, declaring that “We can do more for the people who need it, by doing less for the people who don’t.” (And, notably, he coupled that concern for people who need economic help with a warm embrace of Canada’s ethnic and racial diversity that was starkly different from the Donald Trump-like messaging about immigrants and religious minorities that Harper employed in the final days of the campaign.)
More vital even than the promise of fair and progressive taxation after so many years of Harper’s of-the-rich, for-the rich, by-the-rich governance, however, was Trudeau’s proposal to invest massively in job-creating infrastructure programs. To fund the investment, Trudeau proposed that Canada could and should accept a reasonable level of deficit spending.

Nichols explains, further, that Trudeau made a critical distinction in his messaging: “the fiscal deficit isn’t the one that concerns Canadians and certainly doesn’t concern economists that much. It is the infrastructure deficit that is so concerning to so many people. That’s what’s slowing down our growth.”
And he didn’t shy away from his party affiliation, noting that “The Liberal party is the only party standing straight, looking Canadians in the eye and saying, ‘We need investment and that is what we are going to do to grow the economy, to balance the books in 2019.'”
Like Obama, Nichols adds, Trudeau had a nifty TV ad that went viral:

“At the end of a campaign where they started in third place,” writes Nichols, “Liberals have achieved an absolute majority in Parliament.” It’s the bold emphasis on infrastructure investment, which includes education and retirement of student debt, that appeals to young voters in particular. That and the highly positive tone of his central message:

“We beat fear with hope. We beat cynicism with hard work. We beat negative politics,” Trudeau told the cheering crowd. “In Canada, better is always possible.”

An e-blast from Greenberg Quinlan Rosner Research sheds further light on the historic dimensions of Trudeau’s victory:

No party in Canada has ever come from third place in seats and public opinion standing to win an election since its founding in 1867. The Liberals did it by putting forward an unabashedly progressive alternative that promised real change from the past Conservative decade. Trudeau’s party is also the only party to win seats in every one of Canada’s ten provinces and three territories, a tremendous accomplishment given the regional tensions that have riven Canadian politics for much of its recent history.
GQRR’s Canadian team accomplished their own historic first this cycle in Canada, providing strategy, consulting and research for Canada’s first major progressive independent expenditure campaign. Engage Canada, targeted 74 Conservatives, overachieved its target, as the Conservatives slipped from 188 seats on recently redistricted electoral boundaries to 99.

Another benefit of Trudeau’s big win to President Obama is described by TDS managing editor Ed Kilgore at The Washington Monthly:

And without question, the ejection of Harper is a boon to the Obama administration, especially on energy and environmental issues where Canada had become problematic in its resistance to climate change action and its advocacy of the Keystone XL pipeline.
And Trudeau has some important American links: among the consultants to the Liberal Party for this election were former Obama political staffers Stephanie Cutter, Jen O’Malley Dillon and Teddy Goff.
All in all, it was a good day for the center-left in Canada and elsewhere.

All of the caveats about the different system and electorates of Canada notwithstanding, Trudeau’s creative messaging is instructive, especially for Democrats, who embrace similar policies that helped produced his upset. “With an embrace of progressive taxation, public investment and a humane approach to economics,” concludes Nichols, “Democrats could in 2016 celebrate President Obama’s accomplishments while holding out the promise that, “In America, better is always possible.”