Instructions
Head north to the next area from the starting point in Oho Oasis. This takes you to the Fire Palace --- head up the stairs and into the palace.
Have Luigi stomp on Mario to make him smaller. Walk into the next room through the small opening in the wall. Smash the stone in this room to make the Palace Keeper reveal himself. When he leaves, go up to the fiery orb to gain the Firebrand hand ability. The Palace Keeper returns to give a tutorial on how to use the power. Exit the room through the southeast door.
Use the Firebrand ability to light the small opening in the wall to open a gate. Follow the linear path to meet back up with Luigi, then leave the Fire Palace. Head south, to the southeast portion of the island, then west to a new area. Go north of the new area to find the Thunder Palace.
Enter the Thunder Palace and have Mario pound Luigi. Leave Mario behind and walk under the gate to get to the next room. Use the hammer on the stone, and the Palace Keeper appears. Ignore his scolding and approach the lightning orb to learn the Thunderhand hand ability. The Palace Keeper returns and begrudgingly gives a tutorial on how to use the power.
Exit through the door to the southwest. Use the new ability on the lifeless orb in this room to make the gate open. Follow the linear path to be reunited with Mario.