Before heading inside the Palace, talk to the lady outside near the Palais Lane entrance. She will give you an Oran Berry. Head near the fence of the Palace and pick up the Ether in the far left.
To the lower left of the lower left of the area is the a Photo Spot. You can take a picture if you want.
Head for the gate to enter the Palace. You will be asked for an entrance fee of P1,000 which you will have no choice but to pay.
As you enter, you will be greeted by the sight of a man searching for his Furfrou. Shauna asks you to help look for it.
Let’s explore the palace before looking for Furfrou. The left most room beside the staircase has nothing special in it. The room to its right with the backpacker in front is a bedroom where you and your Pokémon can rest and rejuvenate.
There are no other notable things on the first floor, proceed to the second floor via the staircase to the left. Head to the left and enter the first room to obtain an Amulet Coin. Let your Pokémon hold the Amulet Coin so that you can earn twice as much money after battles.
There are no more items inside the palace, but you can get a nice view of the courtyard by going to the balcony. The balcony is to the left of the room where the Amulet Coin was.
Head back to the first floor and enter the courtyard through the door in the middle.
Enter the southwest area of the courtyard and go to the left to obtain HM01 Cut. Cut enables you to access areas which were not passable before. Head northwest to obtain a Super Potion
Note that a Pokémon cannot forget HM moves unless taken to a Move Deleter. Pokémon with HM moves also cannot be traded to those players who have yet to have that HM for their own
Head north and ignore Furfrou for now. Go to the upper leftmost corner of the area for a Guard Spec.Go back to the entrance of the courtyard and enter the southeast area. In the middle of this area is an Antidote.
Leave the southeast area and head to the east. Go up until you notice a small dirt path. You may not see it if you stick to the right most but there is a hidden Revive amongst the bushes.
Go back to the northwest and enter the area where Furfrou is. As you approach it, it will run away.
You and Shauna will have to work together to catch it. Tell shauna to wait at the entrance where you were standing and approach Furfrou from the lower left. When it runs, move Shauna to the left area while you approach Furfrou form the right.
Once you’ve cornered it, its owner will ask you to meet him at the balcony so that he can reward you.
Head back in to the palace and go to the balcony. Speak with Shauna for a cutscene.
Shauna will then remember what you went there for and mention that you need to wake the Snorlax up. The owner will then hand you over the Poké Flute.
Shauna will then ask the butler about Mega Evolution. He will mention reading about it in the palace library. The palace library is where you obtained the Amulet Coin. You can read about it if you want but there is nothing you can gain from it. Before he leaves, he will give you TM17 Protect.
With the Poké Flute on hand, head back to Route 7 to wake Snorlax up.