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
Next, you need 10 each of Lumber, Fluff, Paper. Read on to learn how to acquire each of these.
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.
Bricks, Gold Ingots, Concrete
You now need to gather 40 Bricks, 20 Gold Ingots, and 50 Concrete.
To get Bricks, give Squishy Clay to a Pokémon with the Burn specialty.
To get Gold Ingots, you needs to find Gold Ore, which can be found in caves in Rocky Ridges, or from the Volcanic Dream Island, which you can reach by checking on an Arcanine Doll and going with Drifloon.
To get Concrete, go through the story in Sparkling Skylands and you will meet Conkeldurr, who will help you set up a concrete mixer. Put Limestone into the mixer to get concrete. Limestone can be found near Tinkmaster's tower, or in the area of Rocky Ridges with the hot spring, or from the Rock Peak Dream Island, which can be reached by checking on a Clefairy Doll.
Electricity, Crystal Fragments, Tinkagears
For the next part, you need 50 units of electricity, 10 Crystal Fragments, and 5 Tinkagears.
For electricity, you can do things like put waterwheels in the waterfall area across from the tower, put furnaces near the tower, and put windmills on the elevated area above the waterfalls. There is a grey stone square with a circle near the tower where you can put a utility pole to connect the generators to the tower. A waterwheel provides 20 units of electricity, and a furnace provides 30.
Crystal Fragments can be found in the lava caves in Rocky Ridges, as well as in the Sky Dream Island, which you can reach with a Dragonite doll.
To get Tinkagears, give Iron Ingots to Tinkmaster in Sparkling Skylands.
Industrial Beds, Resort Lights, Office Desks
Next, you're asked to provide 4 Industrial Beds, 4 Resort Lights, and 4 Office Desks.
You can get the Industrial Bed recipe in the stone-walled area across from the Pokémon Center in Rocky Ridges.
You can get the Resort Light recipe in the building northwest of the Pokémon Center in Bleak Beach.
You can get the Office Desk recipe just south of the Sparkling Skylands Pokémon Center.
Washing Machine, Refrigerator, Game Boy System
You're asked to provide 1 Washing Machine, 1 Refrigerator, and 1 Game Boy System.
After you raise the environment level to 5 in Bleak Beach and complete the important requests there, you receive a Washing Machine, and you can also purchase the Washing Machine recipe from the Bleak Beach PC Shop.
After you raise the environment level to 5 in Rocky Ridges and complete the important requests there, you receive a Refrigerator, and you can also purchase the Refrigerator recipe from the Rocky Ridges PC Shop.
After you raise the environment level to 5 in Sparkling Skylands and complete the important requests there, you receive a Game Boy System, and you can also purchase the Game Boy System recipe from the Sparkling Skylands PC Shop.
Your Cherished Photo
Next, you need to provide a photo that you have taken with the in-game camera. You can either go and take a new one, or just pick an existing one from your album.
Party Poppers
You are asked to provide two party poppers. You learned the recipe earlier in the game.
Congratulations!
After you provide the party poppers to the tower, there will be a cutscene and the credits will roll. Congratulations!
Meet Magneton
Go down the ladder where the tower used to be and talk to the Pokémon to meet Magneton. Build the home they ask for. Control Units can be found on the eastern island of Sparkling Skylands. After they move into the home you create for them, they will teach you Magnet Rise.