In Eterna City, you can get an Explorer Kit from Underground Man. It allows you to enter the Grand Underground, where you can dig for treasure, make a Secret Base, and more.
How to Enter the Grand Underground
The Grand Underground is a network of caves under Sinnoh. After you receive an Explorer Kit from Underground Man in Eterna City, you can enter the Grand Underground any time by using the Explorer Kit from your Key Items Pocket while you are outdoors. You can choose to play in Local mode, Internet mode, or play alone.
If you go to the places marked with a question mark on the map, you will find areas with pokémon wandering around. Approach them to battle them, for a chance to catch them.
Digging For Treasure
If you see a small diamond on the map, go there and press R to reveal the location of a wall where you can dig. Check on the wall there and you can try digging there. This allows you to dig for fossils. The Explorer Kit will tell you how many hidden items are in the wall (this number doesn't include the hard areas that your tools bounce off of). The pickaxe breaks a small area, while the hammer breaks a larger area. Try digging through the layers of the wall until you reveal hidden items. You can keep digging until the crack along the top of the screen reaches the left side. You will collect any items that you revealed in the wall.
You will find people in the Grand Underground, and some of them may trade treasure for items.
How to Leave the Grand Underground
You can leave the Grand Underground any time by pressing Y. The first time you leave, Underground Man will give you some Spheres.
Talk to Underground Man after you have dug up some spheres and fossils in the Grand Underground, and he will give you the Digger Drill. You can use it while in the Grand Underground to create your Secret Base. Just check on a wall to use it, then check on the door that you drilled to enter your Secret Base.
In your Secret Base, you can place statues that you find in the walls of the Grand Underground. These statues can cause certain effects, like increasing the appearance rate of certain types of pokémon.
Press Y while in your Secret Base to switch to free camera movement.
Decorate Your Secret Base
You can find statues while digging for treasure, and you can place the statues in your Secret Base to boost the likelihood of encountering certain types of pokémon.
If you play in Internet mode or local mode, you can enter other players' Secret Bases and check on the orb there to use the effect of their statues.
At junctions and corners in the Grand Underground, there is a chance of finding a Diglett or a Dugtrio. These will drop sparkles, which will add to the gauge below the map. When this gauge is full, there is an increased chance of finding rare treasure.
How to Move Your Secret Base
You can move your Secret Base by getting another Digger Drill. Just look for a trader in the Grand Underground and trade spheres with them to get a Digger Drill.
Rewards From Underground Man
After you create your Secret Base, talk to Underground Man in Eterna City to get some Quick Balls, Dusk Balls, and Dive Balls.
Then, after you decorate your Secret Base, talk to Underground Man again to get a Square Pedestal XS.
Then, if you enter the Grand Underground in Internet mode or Local mode, and if you enter someone else's secret base, go back and talk to Underground Man to get a Round Pedestal M and a Sturdy Pedestal S.
If you once again enter the Grand Underground in Internet mode or Local mode and find different colors of lights in the walls from the usual yellow ones, you can dig there to find better treasure from usual. After you dig in one of these different color spots, go back and talk to Underground Man