The Princess’ Secret Slide is accessible through a door up the stairs and to the right of the large locked door. You will require at least one Power Star in order to enter the room, where you will find three windows with Princess Peach’s image on them. The window on the right when your back is to the door is false, so you can go through it to arrive at the secret slide. You might see a Blue Coin Block in the area before the actual slide, but you don’t benefit from it, as this classifies as one of the castle’s secret stars. All of the secret stars are in one-off areas, meaning there’s usually only a single star in these areas.
For Princess’ Secret Slide, though, there’s actually two stars here, one for completing the slide itself and another for finishing it under a specific time. Read the sign before the actual slide begins to get a gist of the controls, where you tilt the left analog forward to speed up or pull it down to slow Mario. As soon as you start sliding on the track, the timer will begin, but it’s best to run it a few times to get a feel for the layout. There’s nothing too special about the slide itself, although you won’t have any rails on the side for the middle portion, so you could fall down into the abyss.
Thankfully, you don’t lose any lives for falling into the abyss, with Mario just being deposited in the main hub. At the end, you will find a yellow box that contains a Power Star. The other, more hidden, star requires you to finish the course in under 21 seconds. You should be tilting the left analog stick forward for the majority of the slide, and cutting corners as much as possible. You just need to keep going until you get under 21 seconds, with the star spawning as soon as you cross the finish line under that time.