You cannot sell items in the normal sense, but you can trade them.
By placing a cash register, which you can find in places that previously had a shop (Do some exploration, you'll find a few on your travels) and get a Pokémon with the ability to trade, it will set up a shop, at which point you can trade. A cash register needs to be near a power source to work. You can also restore any given Pokémon center and it will have a cash register sitting there.
To trade, walk up to the surface your cash register is on, and interact with one of the items available to trade.
A given item will have a certain amount of "Trade Points". In order to successfully trade, you must reach or surpass this number with items and materials of your own.
EX: 10 Chesto Berries has a value of 500 Trade Points. So Vine Ropes, which have a value of 10, could be used in combination with Beans, which have a value of 50. So you would need 10 Beans or 50 Vine Ropes, or some combination of the two.
Hope this helped!
Source: https://www.nintendolife.com/guides/pokemon-pokopia-trade-guide-how-to-buy-items-from-pokemon
