In order to advance through Pokémon Legends: Arceus, you’ll need to conduct research tasks. And in order to turn those tasks into money to buy some new fashionable clothes, you’ll need to turn in your research. Just as in real life, turning in your research is not so simple as congratulating yourself on a job well done.
In order to turn in your research and get that sweet, sweet science money, you need to find Professor Laventon. On your very first outing for the Survey Corps, he’ll be right at the base camp. If he’s not so conveniently hanging around, you can find him in his office, which is on the first floor of Galaxy Hall in Jubilife Village. His office is directly to the right of Cyllene’s — even sharing a door with her. Simply talk to Laventon with the A button, and he’ll start inquiring about your research.
Note that the more research tasks you complete, the more money Laventon will give you. Additionally, if you complete certain tasks, like catching a Pokémon for the first time, your payday will go up, too. Your Star Rank also affects your payout: the higher your rank, the more money you make per task.