“Joining the Stormcloaks” is a Stormcloaks Faction Quest in The Elder Scrolls V: Skyrim
Having passed through Windhelm and spoken with Ulfric Stormcloak and Galmar Stone-Fist, the Dragonborn is sent off to be tested. They want the Dragonborn to go to Serpentstone Isle and slay an Ice Wraith there to prove themself. Talking with Galmar Stone-Fist, he will give you an Elixir of Resist Cold and 3 Ice Wraith Banes. He explains that is all the help he will give you.
It is a bit of a trek to Serpentstone Isle, found a bit to the North of Winterhold. Travel your way to the North. Swim out to the marked island. You can also find the Serpent Stone on this island to get its blessing if you desire it.
Once on the island, you just need to track down and kill the Ice Wraith that haunts it. It tends to be very close to the Serpent Stone. That makes it a bit easier to find. It helps a lot to use the Elixir of Resist Cold. Attack with Fire-type attacks and the Ice Wraith will go down without any trouble.