Short answers, pulled from the story.
The Abdications of Bayonne took place on the 5th, 6th, and the 7th of May 1808 at the castle of Marracq in Bayonne, France. Charles IV signed away the Spanish Crown on May 5 and Ferdinand VII formally renounced his rights by May 6.
Napoleon forced the abdications to replace the Bourbon dynasty with a member of his own family and bind Spain firmly to his imperial system. The instability revealed by the Escorial Conspiracy of 1807 and the Tumult of Aranjuez in March 1808 convinced him the Bourbons could not be trusted as allies.
Napoleon transferred the Spanish Crown to his brother Joseph Bonaparte, who had previously been King of Naples since 1806. Joseph I entered Madrid on the 20th of July 1808, but was forced to leave eleven days later after the French defeat at the Battle of Bailén.
The abdications were rejected throughout Spain and Spanish America by those known as patriots, who refused to recognise Joseph I and maintained loyalty to the captive Ferdinand VII. The Council of Castile declared the abdications null after the Battle of Bailén, and Ferdinand VII was proclaimed king in absentia on the 24th of August 1808.
Charles IV agreed to cede his rights to the Spanish Crown to Napoleon on two conditions: that the territorial integrity of the monarchy be maintained, and that Catholicism remain the kingdom's sole religion. In return, Napoleon committed to hosting Charles IV, his wife, and Manuel Godoy in France, paying them 30 million reales monthly and granting Charles IV the Château de Chambord.
The abdications triggered the Peninsular War of 1808-1814, which became a contributing factor to Napoleon's final defeat. Napoleon was eventually forced to release Ferdinand VII and restore him as King of Spain through the Treaty of Valençay on the 11th of December 1813.