Short answers, pulled from the story.
Horace Greeley ran against Ulysses S. Grant in 1872, standing as the joint nominee of the Democratic Party and the Liberal Republicans. The Liberal Republicans were a breakaway faction that split from the Republican Party over corruption and Reconstruction policy.
Horace Greeley won the Liberal Republican nomination after early front-runner David Davis lost support and Charles Francis Adams, Sr. failed to hold his early lead. Benjamin Gratz Brown dropped out of the race and endorsed Greeley, who then overtook Adams and won with 482 delegates to Adams's 187.
Horace Greeley lost to Ulysses S. Grant in a landslide. Grant carried 31 of the 37 states, won the Electoral College 286-66, and won the popular vote 55.6-43.8%, the highest winning percentage of any election between 1828 and 1904.
Benjamin Gratz Brown embarrassed the Greeley campaign by attending events and giving speeches while intoxicated. He fainted before a gathering in New York City and was seen slicing and buttering a watermelon while drunk at a campaign picnic, and he sometimes forgot the party's own policies.
Horace Greeley died several weeks after the 1872 election, before the Electoral College met to formalize the result. His death followed exhaustion and demoralization from the campaign.
A faction calling itself the Straight-Out Democratic Party rejected Horace Greeley's nomination and held its own convention in Louisville, Kentucky. It nominated Charles O'Conor and John Quincy Adams II, though both men disavowed the effort, and its electors drew just 0.35% of the popular vote.