Short answers, pulled from the story.
The Battle of Ligny was fought on the 16th of June 1815 near the village of Ligny in what is now Belgium. The battlefield lay on the watershed between the rivers Scheldt and Meuse, along a narrow stream that ran through the villages of Ligny, Saint-Amand, and Wagnelée.
The Battle of Ligny was a tactical French victory. Napoleon's forces, numbering around 60,800 troops, defeated a Prussian army of 82,700 under Field Marshal Blücher. French trophies consisted of 21 guns and a few thousand prisoners, but the bulk of the Prussian army survived and retreated in good order.
Ligny was the last battle Napoleon ever won. Despite the French victory, the Prussians retreated northward rather than east, keeping them within supporting distance of Wellington. Two days later on the 18th of June 1815, Blücher's army marched to Waterloo and helped defeat Napoleon decisively.
Field Marshal Blücher, then 72 years old, was personally leading a cavalry charge when his horse was shot and fell on top of him. He was dragged out semi-conscious and removed from the field. His chief of staff, Lieutenant-General Gneisenau, took command for the remainder of the battle.
D'Erlon's I Corps played no role in the fighting, despite being ordered east toward Ligny by Bédoyère acting on Napoleon's instructions. Marshal Ney, unaware of those orders, countermanded them and directed d'Erlon to march back toward Quatre Bras. The corps spent the day marching between both battles and fought in neither.
The Prussians retreated northward to Wavre rather than east along their lines of communication, a decision associated with Blücher's insistence on staying close to Wellington. Zieten's I Corps left a rear-guard near Brye until daybreak on the 17th of June. The army regrouped south of Wavre, roughly 8 miles east of Waterloo, and marched from there to join Wellington on the 18th.