You don't get much time to celebrate your victory against Lenora, because after receiving your badge, Hawes rushes down to Lenora's room and says that Team Plasma is in the museum, threatening to steal some bones. Lenora will rush upstairs.
When you follow, you and Lenora and Hawes will watch as Team Plasma steals the Dragonite fossil skull and runs away.
Go outside, and Burgh will ask Lenora what's up. Burgh is the leader of the Castelia City gym. Cheren and Bianca also show up. Burgh says that he will help look for Team Plasma. Lenora tells Cheren and Bianca to guard the museum. Bianca gives you the Dowsing Machine, which is a very helpful device that I'll say more about in a moment. Lenora heads to the entrance of town to look for Team Plasma and asks you and Burgh to check Pinwheel Forest.
How to use the Dowsing Machine
When you use the Dowsing Machine, a special display will show up on the bottom screen. There are two sticks in the picture, and if you are close to a hidden object, the machine will make a noise and the sticks will point in the direction of the hidden object. When you are standing on the object, the machine will beep and display a square in the middle. In order to actually pick up the object, you can't be standing on it. You have to go one square away from it and check that square in order to get the object. It's a good idea to leave the machine on at all times if you're in a new area or a place where you haven't had the Dowsing Machine in the past.
Looking for Team Plasma in Pinwheel Forest
Anyway, head on over to the inside of Pinwheel Forest. It's no longer blocked off by Team Plasma grunts. Burgh will tell you that there are two paths through the forest: one is a straightforward path going north, and the other is a winding path that starts to the west of where you're standing. Burgh will check out the north path and he will ask you to investigate the west path. He says that if he doesn't find Team Plasma to the north, he will block the northern exit.
By the way, in the grass in Pinwheel Forest, you can find Sewaddle, Cottonee (Black version only) or Petilil (White version only), Venipede, and occasionally Pidove. In shaking grass, you can find the three elemental monkeys (Pansage, Pansear, Panpour.)
Anyway, even though Burgh said that he'll go north, you should also go north to fight the trainers that are there. The Dowsing Machine will beep near a river, but you can't reach the hidden item right now.
When you're done fighting the trainers to the north, go back down to the winding path that is west from the forest entrance. There will be some twins here that you have to fight. The forest path is pretty straightforward here, so just go around fighting trainers. Occasionally a Pokémon Ranger will pop out from a hidden place and challenge you.
If you need a heal up, talk to the Nurse just outside of the forest entrance.
After making your way through the winding path and fighting the trainers and Team Plasma grunts there, you will reach a clearing after passing through a couple of hollow logs. A Team Plasma grunt is here. This one has two Patrats and a Sandile. The Sandile is Ground/Dark. As such, it is weak to Fighting, Bug, Water, Grass, and Ice, strong against Poison, Rock, Ghost, and Dark, and is completely immune to Psychic and Electric moves.
By now you should have Bug and Grass pokémon from the forest, as well as Fighting-types that you used in the previous gym. If your starter is Oshawott or Snivy, bring it to the battle as well. Be sure not to bring Venipede, though, because its Poison-type makes it vulnerable to Sandile's Sand Tomb move.
Retrieving the Dragon Skull
This battle shouldn't be too tough. Once you defeat the grunt, he will return the dragon skull. He will say that without the skull, the dream of Team Plasma's king won't come true. Then Gorm, one of the Seven Sages of Team Plasma, will arrive and say that it doesn't matter that they have lost the skull, because their research says that it is not the legendary pokémon that they are looking for.
Burgh and Lenora arrive at the scene, and Gorm and the grunt leave. Burgh will go back to his gym at Castelia City, which is your next destination. Lenora gives you a Moon Stone in thanks for returning the Dragon Skull to her. After she departs, you can head east to get a Miracle Seed. Then, if you are ready, you can go through the north exit of Pinwheel Forest.