For this trick, you need to have a full occupation of 10 villagers on your island, which may take a little while if you are still on a mission with Tom Nook early in the game. Until you build the camp and start selling land to potential residents, you can maximize the population of the town.
Once you have a complete roster, the next thing you need is an Amiibo card for the villager you want to exchange. You can also wait for a villager to appear in the camp, but this method at least guarantees the appearance. Rare villagers, even if you have enough Animal Crossing Bells For Sale you may not be able to buy them.
Use Amiibo Cards to summon the villagers to the campsite, create any DIY projects they want, make them happy, and make sure to do so within 3 days, because they have been dissatisfied with entering the island until you give them enough help .
On the third day, give them the last gift and talk until you convince them to move in-only they will come back sadly because there is no space on the island. At this point, they will mention that they have heard that someone is considering moving-this is your big opportunity. ACBellsBuy people provide plenty of items for players to choose from. You can also Buy ACNH Nook Miles Tickets in exchange for the villagers you need in the game.
They will let you point out the villagers who are willing to "negotiate" to move out, let new villagers move in, and kick your problem residents out! Once you choose to kick out the villager, your new friends will easily know that they are considering leaving at any time and will prepare for moving in. You can even go and chat with the people you are about to become former residents who are already packing their bags.