Professor Laventon asks for you to help him with research tasks in Obsidian Fieldlands.
Go to Fieldlands Camp
Go to the east exit of Jubilife Village and choose the Fieldlands Camp as your destination. There will be a cutscene where you learn about checking a wild pokémon's research tasks, and how to dodge. You can check the Survey Tips in the Settings section of your satchel to review this information.
Follow Rei or Akari
Go to the guidance marker (you can open the map and press Y to change which mission or request has guidance enabled) to find Rei or Akari. They will tell you to use ZL to focus on a wild pokémon, then press down to open the pokédex to that pokémon's entry, so you can review the research tasks. This also adds that pokémon to the Pokédex, so you can have some of its information even if you don't catch it. Be sure to do this with every pokémon you encounter outside of battle.
As you go through the area, keep an eye out for plants that you can gather, and trees that you can throw your partner pokémon at to gather things like Apricorns and Oran Berries.
There are three Bidoofs in the area. You can catch them or defeat them to complete some of your research tasks.
When you are ready to move on, go to the guidance marker to find Rei or Akari. There will be another cutscene, where they remind you to check your research tasks and try to catch a Starly without being seen. After you are done catching Starly, go to the guidance marker and there will be another cutscene.
Next, you are asked to catch a Buizel. You will need to battle it first, so be sure to throw a partner pokémon instead of a Poké Ball.
When you are ready, go to the guidance marker for another cutscene with Rei or Akari. You will get a Crafting Kit. You can use it to craft things wherever you are, but you will only be able to use the materials in your satchel. You will also get the recipe for crafting Potions. To use the Crafting Kit, look in the Key Items section of your Satchel (press R to switch between Everyday Items and Key Items).
Report to Professor Laventon
Feel free to explore the area and catch or battle more pokémon. When you are ready, go to the guidance marker to return to Professor Laventon and report the research tasks that you have completed.
You will receive money whenever you submit survey reports, with a bonus for completing certain research tasks.
You can also rank up in the Galaxy Expedition Team after accumulating a certain number of Pokémon research points.
If you haven't gotten enough points to rank up yet, the Professor will recommend which pokémon's research tasks you should focus on. You'll need to rank up to complete this mission.
Report to Cyllene
Once you have enough points to rank up, talk to Professor Laventon and you will automatically return to the village. Go into the Galaxy Team building and talk to Cyllene, then exit the Pokédex to continue. You will get the rank of First Star. This unlocks the use of the Heavy Ball, and pokémon up to level 20 will obey you in battle. You will also earn more money for research reports. Cyllene will give you recipes for the Heavy Ball, and Revives.
After a cutscene, Rei or Akari will ask you to battle them at the Training Grounds. This begins the mission A Request from Mai.