Short answers, pulled from the story.
The Battle of Trafalgar took place on the 21st of October 1805 in the Atlantic Ocean off the southwest coast of Spain, near Cape Trafalgar. The British fleet engaged the combined French and Spanish navies during the War of the Third Coalition.
Nelson sailed his fleet in two columns directly at the Franco-Spanish battle line, cutting it into three sections. This broke the conventional single-line approach and forced a ship-to-ship melee in which British crews' superior gunnery and seamanship gave them an advantage.
Nelson was shot by a musket bullet fired from the mizzentop of the French ship Redoutable. The bullet struck his left shoulder, passed through his spine at the sixth and seventh thoracic vertebrae, and lodged below his right scapula. He died at half-past four on the 21st of October 1805, three hours after being hit.
Villeneuve was captured along with his flagship Bucentaure and taken to Britain, where he attended Nelson's state funeral as a captive on parole. After his parole in 1806, he returned to France and was found dead in his inn room with six stab wounds in his chest from a dining knife; his death was officially recorded as suicide.
The British fleet under Nelson had 27 ships of the line, while the combined French and Spanish fleet under Villeneuve had 33 ships of the line. The allied fleet also included the Santísima Trinidad, the largest warship present, a Spanish first-rate carrying 130 guns.
Britain captured or destroyed 18-20 allied ships while losing none of its own. The victory confirmed British naval supremacy, though it had limited impact on the broader war. Less than two months later, Napoleon defeated the Third Coalition at the Battle of Austerlitz, and the Napoleonic Wars continued for another ten years.