be more specific what do you want to know about Zants invasion of Hyrule?
After obtaining power from Ganondorf and usurping the throne from Midna, Zant launched an invasion of Hyrule, because he wanted to avenge his ancestors, the Interlopers, and take back the land that he believed rightfully belonged to them.
Alright i'll try mentioning it all in detail: Zant is not able to overthrow the twili "royal" family, he then receives some power from ganondorf and is able overthrow the royal twili's, turning midna into an imp, and turning twili's into shadow beast. He then goes to conquer the lands he believes are his and launches a military campaign against hyrule, where he most likely (this is my believe) first started by invading the Desert, where he found a settlement of bulblin's who allied to him, he then goes into zora's domain, where rutela refuses to surrender to zant's army, who he later after conquering the zora's, executes infront of her people, and then punishes the zora's for their resistance by freezing lake hylia (with the power ganondorf gave him). He then goes into the castle and forces zelda to surrender, after her surrender, he decides to turn the light world into twilight and steals the Lanayru light spirits. After finding out about the second light spirit location, he sends his troops into kakariko, where he is *most likely* either met by a small militia made up of the citizens of the village, or decides to go in a killing spree because of the weakness of those living there. After most of the inhabitants are killed he steals the light spirit of Eldin, and heads southward into Faron to get the light spirit, which he gets between the time where Link goes and saves Talon, until the time when the children are captured. After conquering most of hyrule he decides he wants to capture it all, and heads to ordona, but here before he can take the light spirit of Ordona he is stop from taking it by Link, and the rest is history