So they set out to reach them in their communities, talking to them in their language, with the belief that touching them in the most personal way possible, at churches, bodegas, bus stops and nail salons, was also the most persuasive. And the effort was focused on more than registering potential voters. Democrats sought to make electoral politics part of the daily conversation for a demographic that had until now largely sat on the sidelines.

Starting in Nevada, the campaign convened groups of women to discuss issues that were important to them, like health care and education. After each meeting, the women were asked to write down the names and contacts of five other women who might support Mrs. Clinton. The program, called “Mujeres in Politics,” was deemed such a success that the campaign replicated it in Colorado and other states with large Hispanic populations.

“We understand this community. We know culturally what are the strongest messages that work for them,” said Lorella Praeli, Mrs. Clinton’s national director of Latino outreach, who had lived undocumented for years after coming to this country from Peru but is now an American citizen. “This wasn’t created in an office. This was built on the ground.”

Mrs. Clinton also had to grapple with the fact that many Latino voters were disappointed with Mr. Obama, who had increased deportations and failed to bring about an overhaul of the country’s immigration laws. Mrs. Clinton knew she would need to tell Latino voters at the start of her presidential campaign that she would go further than Mr. Obama in extending a path to citizenship, even if it meant upsetting the president.

Mrs. Clinton and her Democratic allies now have a presence in every state with a large Hispanic population with customized strategies for each.

In Florida, the campaign identified early on the influx of Puerto Ricans who had fled the island amid its economic crisis as a potential bloc of new Democratic voters. Both Bill Clinton and Amanda Renteria, the campaign’s political director, were dispatched to Puerto Rico. And the campaign issued bilingual messages of support for funding to combat the spread of the Zika virus and to encourage legislation to address the debt crisis in Puerto Rico.