Short answers, pulled from the story.
General Jean-Andoche Junot commanded the French invasion force. He had previously served as Portugal's ambassador in 1805, and Napoleon promised him a dukedom and a marshal's baton if the assignment succeeded. His corps of nearly 25,000 men occupied Lisbon on the 30th of November 1807.
Napoleon invaded Portugal because it was Britain's oldest ally in Europe, the Royal Navy used Lisbon's harbour against France, British trade with Brazil was growing through Portuguese connections, and Portugal refused to fully comply with Napoleon's Continental System excluding British trade. Napoleon also wanted to seize the Portuguese fleet, which included fourteen ships of the line and eleven frigates.
Portugal offered virtually no military resistance. The Portuguese army was undermanned due to decades of corruption and embezzlement, with real strength possibly as low as 20,000 men despite a nominal roll of 48,396. The government never mobilised its forces, and 1,500 exhausted French troops entered Lisbon on the 30th of November 1807 without firing a shot.
Prince Regent John, the future King John VI, fled to Brazil aboard an Anglo-Portuguese fleet of fifteen warships and more than twenty transports. The fleet weighed anchor on the 29th of November 1807, the day before Junot's troops entered Lisbon. The departure was so hurried that fourteen carts loaded with treasure were left behind on the docks.
The Treaty of Fontainebleau, signed in October 1807, proposed dividing Portugal into three parts. The north around Porto would become the Kingdom of Northern Lusitania under Charles Louis of Etruria, the south would become the Principality of the Algarves under Manuel de Godoy, and the centre around Lisbon would remain under French administration. Napoleon is widely believed never to have intended to honour its terms.
The Portuguese army's nominal strength was 48,396 men, but actual numbers may have been as low as 20,000 by 1807. Officers had long collected pay for absent or fictitious soldiers, leaving units chronically understrength, cavalry without horses, and depots without supplies. The army had been modernised by William, Count of Schaumburg-Lippe in 1762, but the reforms were undermined by corruption that resumed almost immediately afterward.