This cave is very dark. To light it up you need to use Flash. You can teach it to your Pokemon with TM 70, which is given away in Castelia City's Narrow Alley. Go south to the boulder and move it into the nearby hole to find some stairs leading to a Hiker.
Walk east to another boulder. Cross the hole to find a Veteran that won't let you pass. Walk north and pick up the Dusk Ball, which is more effective in dark areas like this cave. Go west to another Hiker.
Walk down the stairs southeast of the Ace Trainer and push the boulder into its hole. There is a Green Shard hidden in a rock to the southeast. Walk north up the nearby stairs and follow the path to another set of stairs. Here, going south leads to a Super Potion, while going north leads to another boulder. Past this boulder to the west is the staircase to the third floor. Before heading up the stairs, there is still some more stuff on this floor. Continue north from the boulder to battle another Ace Trainer.
Taking the path up the stairs north of the Ace Trainer leads to a Blue Shard. Following the narrow path west of her leads to a hidden Ultra Ball against the room's western wall. Use the stairs to the third floor.
The item you can see northeast of the floor's entrance is an Escape Rope, which will come in handy to easily return to Route 6. There's a Full Heal hidden in a rock west of the floor's entrance. You can also get TM 80 Rock Slide by hugging the east wall and going to the northeast corner of the floor. Rock Slide deals damage and has a 30% chance of making the target flinch. Make your way to the center of the room to push some more boulders around. To the west is an old man. In the rock behind him is a Dragon Gem. Gems increase the power of a move of the same type by 50%. Unfortunately, gems are a one-time use item. That's everything in the Mistralton Cave for now. Eventually you can come back and pass by that Veteran on the first floor, but for now go back outside and head to Chargestone Cave at the north end of Route 6.