After you learn Rock Smash, you can go to the southern area of Withered Wastelands and find a mysterious box that asks for supplies as part of the Team Initiation Challenge.
How to Find the Team Initiation Challenge Building
Learn Rock Smash (see List of Dittos Moves for instruction on how to learn it), then break the rocks in the southern part of Withered Wasteland. After you progress through the Withered Wasteland story, Professor Tangrowth will want to visit the building in the southern part of Withered Wasteland. Check on the box and it will ask you for items.
Leppa Berries
Use Water Gun on withered trees in the Withered Wasteland to turn them into Leppa Trees, then press A to headbutt the trees to make the Leppa Berries fall off, then pick them up. When you have at least 5 Leppa Berries, check on the box on the building, select Leppa Berries, then use the buttons displayed in the bottom-right of the screen to put the berries in, then choose Submit. You'll get the Bouldery Badge.
Beans, Tomatoes, Wheat
Learn Rototiller (see List of Dittos Moves for instruction on how to learn it), then use it to till the soil so you can plant seeds. You need to harvest 10 beans, 10 tomatoes, and 10 wheat. Wheat can be found in Rocky Ridges, which you can reach from the northwest area gate in Withered Wasteland after you meet Kyogre, and tomatoes can be found in Bleak Beach, which you can reach from the east area gate in Withered Wasteland after you meet Kyogre.
Lumber, Fluff, Paper
To get lumber, you can use Cut on trees or piles of wood, then give the logs to a Pokémon who has the Chop ability. You can search for Pokémon by ability by opening the Pokédex and pressing Y.
To get Fluff, you can either buy some from a Pokémon Center PC for 50 Life Coins, or you can block the flooding in Bleak Beach to reveal a Knitting Station habitat, which will make Mareep or Flaaffy move in. They will occasionally drop fluff.
To get Paper, you have to unlock Sparkling Skylands by meeting both Volcanion in Rocky Ridges and Entei in Bleak Beach to raise your Trainer Rank to Ultra. Then you can access Sparkling Skylands from either the north gate in Withered Wasteland or the northeast gate in Rocky Ridges. You will find Wastepaper in Sparkling Skylands, which you can give to Pokémon with the Recycle ability to turn it into Paper.