- "An invasion of Naboo can mean only one thing. A communications disruption."
- ―Sio Bibble
It started with a dispute about taxation of trade routes. "Tax bad!" "Tax good!" "You not count regulation, which hidden tax!" "That not true! You greedy!" "You strangle business!" "You hate common man!" "You rape babies!" "You rape babies!" And long story short, the Trade Federation struck out at the Republic by blockading Nabooboo. Nobody really understood why. Seriously, not even the Trade Federation understood why. OK, so all the taxes were causing the greedy Trade Federation to lose money, so they react by... blockading Naboo and preventing all trade... which is how they make money in the first place.
Good-hearted Supreme Chancellor Finis Valorum, the respected, the just, the handsome, the thoroughly impotent, reacted by dispatching two Jedi Knights to settle the pointless conflict. That's pretty much how all conflicts were resolved when Valorum was Chancellor, because the Jedi were the only ones with any balls. So Qui-Gon Jinn, hippie extraordinaire, and Obi-Wan Kenobi, the trainspotter, went to meet with Nute Gunray on his medical donut pillow ship.
Nute Gunray was very polite, collected the fees for docking on his ship, collected the fees for entering the star system, collected the transaction fee, collected the non-Trade Federation membership fee, and sat them down in a waiting room with some tea. Then Darth Sidious ordered Gunray to start a ground invasion and kill the Jedi, so he flooded their room with poison gas. Oh, the point here is that the whole invasion was Darth Sidious's idea... and that's the reason it makes absolutely no sense. So the poison gas fails, and Gunray tries killing the Jedi with... B1 battle droids. Go ahead and read the article on those guys to discover why this tactic fails. They send a few droidekas, too, but too late. The Jedi escape and sneak down to the ground.
Unfortunately, they immediately bump into Jar Jar Binks and don't kill him. They hurry to warn the Naboo government of the invasion... and they have plenty of time, because for some reason the Trade Federation landed their invasion force on the other side of the planet. Jar Jar leads them to Otoh Gunga, the underwater bubble-fart Gungan city, and they give them a bongo... which the Jedi use to play Babaloo.
Meanwhile, the Trade Federation "army"... mostly worthless B1 battle droids, but also some fairly powerful AATs, which sort of look like mini-vacuum cleaners... actually, all the Trade Federation vehicles look like vacuum cleaners. They invade the Naboo city of Theed, which offered absolutely no resistance, because Queen Amidala and her trusted lieutenant Panaka were complete pussies. Qui-Gon, Obi-Wan, Amidala, and Panaka all agree it's time to get outta here Scooby! and they utterly fail to leave Jar Jar behind.
They go to Tatooine and waste time and pick up an annoying young Anakin Skywalker ("yippee!") and his annoying droid C-3PO... well, that was pointless. Then they waste more time on Coruscant and give speeches in the senate... even more pointless. Then they return to Naboo and defeat the Trade Federation by playing a quick game of Castlevania. The Theed Palace was mostly empty because Jar Jar and his helpful Gungans died by the thousands in a diversionary attack. Nice of them. Darth Maul showed up out of nowhere and killed Qui-Gon Jinn, but that's not really part of the "Invasion of Naboo," per se. Anakin Skywalker blew up a command ship with an N-1 starfighter... which was the same color as the short bus he rode to school every day.
Then they won and everybody cheered and they held a glowing ball up in the air. But it was all according to Palpatine's evil plan. Glowing ball. A ball that glows.