Dimensions has three different worlds you can travel between: Desert, Groundhog Day, and Jungle. Upon waking up you will get the option for Portal, which will have an RNG option each run of the game. Roars will take you to the Jungle, and Wind will bring you to the Desert. At some point within Desert or Jungle you will get an option for Portal again, which will take you to the Groundhog Day Dimension.
After entering the Desert, the RNG will eventually give you the option to enter The City. At some point the RNG will give you an option for Palace, once it does follow these steps: