There are 3 ways to get an everstone in Pokemon SoulSilver:
1. Show Professor Elm a Togepi (which you get by obtaining the mystery egg from Professor Oak in Cherrygrove City).
2. Come second in a bug catching contest.
3. In Kanto, go to Route 25 and show Bill's grandfather a Lickitung.
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Prof. Elm will give you one if you show him the Pokemon that hatched from the egg (aka Togepi)
No Pokemon evolves with an everstone. In fact, an everstone negates the effects of evolution if you give it to a Pokemon to hold.
The everstone stops evolving all Pokemon that evolve in the first place.
What u do with a everstone is u give it to a Pokemon and it wont evolve
In Pokemon Blue, the Everstone can be obtained by defeating wild Geodudes and Gravelers in Rock Tunnel. These Pokemon have a 5% chance of holding an Everstone when encountered. The Everstone prevents a Pokemon from evolving when held, making it useful for trainers who want to keep a particular form or moveset. Remember to save your game before battling these Pokemon to increase your chances of obtaining an Everstone.