Gunther, of the Stardew Valley Museum and Library, has the key to the Sewers but he won’t hand it over until you can donate 60 Artifacts or Minerals to the Museum’s collection.
These are mostly found in the Mines by cracking opening Geodes but occasionally you’ll find them from digging in the ground. Either way they’ll take quite some time to find.
The day after you have donated your 60th item Gunther will visit your house and give you the Rusty Key for the Sewer.
There is an NPC in the Sewer named Krobus. He looks pretty scary but he’s actually pretty friendly and has a number of items for sale including a Stardrop.
The Sewer is also home to the legendary Mutant Carp. A rare fish that is worth 1.250 Gold if you catch it. There’s also plenty of regular carp down in the Sewer if you enjoy fishing.
Head back to the Stardew Valley Walkthrough here.