The Mysterious Tower is by far the shortest world on the entire game. Unlike Kingdom Hearts II, only the countryside, the main entrance, and the chamber are accessible.
Upon completing Enchanted Dominion, Dwarf Woodlands, and Castle of Dreams, go to the Mysterious Tower so Terra can speak to Yen Sid about "a boy in a mask controlling the Unversed" and Master Xehanort's disappearance. Go to the tower on the world map, select "visit this world", and a cutscene will play. Mickey is shown taking off with the Star Shard and the Star Seeker Keyblade.
Before going inside, fight some Unversed and unlock some treasures. Then, go inside to open a big chest. Next, go up the stairs. The stairs will directly take you to Yen Sid's chamber. A cutscene will play in which the two men speak about Mickey's intentions, and if Master Xehanort and the Unversed are "one and the same problem." Yen Sid suggests Terra to find Master Xehanort first. Once the cutscene is over, Xehanort will call Terra over to another world.
After visiting Yen Sid, don't forget to pick up a sticker in his chamber.