If you have played Pokemon Diamond, Pearl, or Platinum, you may remember the Explorer Kit that allows you to dig for treasure and do other things underground. In Soul Silver, it's not possible but you can still get those items you found Underground.
Of course the first way to do it is to find the item somewhere in Johto or Kanto looking like a Pokeball on the ground or by finding the items hidden...somewhere.
The main way you want to do this includes destroying rocks by using the HM move Rock Smash.
When destroying a rock by using Rock Smash, there is a possibility of finding an item in the rubble or encountering a Pokemon.
Some Pokemon you may encounter would be Crabby, Geodude, Graveler, and Shuckle.
Some items you may find are usually Fossils, Shards, Revives, and items that could be sold for a lot of money...like the Rare Bone.
Some places where you will find these rocks would be the Ruins of Alph, Cliff Cave, and Victory Road.
Finally, if you didn't find anything when destroying the rocks walk out of the room and the rocks will reappear so you can try to find some items or Pokemon again.