How do you get to sky rift?

after going through azurill's nightmare just go to sleep (in the game not in reality) palkia should attack you and your partner and take you to sky rift.

There are 15 basement floors until you reach a Kangaskhan rock, then 9 more floors until the bottom.

Fist of all, its Spacial Rift, not Sky Rift. You have to complete the main story first, start the post game story, find and take care of Manaphy (you get it as a Wonder Egg in the Surrounded Sea),...

Follow the questline.

You should already have spacial rift on your list.