With 397 confirmed villagers in Animal Crossing: New Horizons, there are plenty of villagers to choose from when inviting them to your island. Moving a villager in is fairly simple, but moving them out can be a little more tedious.
How to Invite New Villagers to Your Island
In previous Animal Crossing games, villagers would randomly move into your town with their own house and furniture. It's a little different in New Horizons.
When you first arrive on your island, you will start with two villagers, and as you slowly progress through the game, the max number of villagers allowed on the island is 10 (including other player characters).
The Resident Representative chooses the plot of land for the two starting villagers. After that, Tom Nook will send you on a mission to place three homes and craft furniture for the new residents. All of this must be done before the new villager can move to your island.
After this task, inviting villagers will always require 10,000 Bells to place a plot of land for the new villager, and you're on your own to invite new villagers to the island.
Here are two methods to invite villagers to your island.
Mystery Island
Have you had a chance to use the Nook Miles Ticket? By using the Nook Miles Ticket (exchanged at the Nook Stop in Resident Services), the airport will drop you off at a randomly generated island that will (sometimes) have a villager who can be invited to live on your island.
You will be presented with the option to invite the villager to your island after talking to the villager twice. By talking to them, you can also discourage them from moving to your island.
If you decide to invite a villager to your island before Tom Nook assigns you with the task to place the three homes, a villager you invite from a Mystery Island will be included in his list. If you invite a villager and you haven't placed a plot of land on your island, they will move in once a new plot of land is placed, or if a villager moves out.
The Nook Miles Ticket is 2,000 Bells, so if you're planning on inviting a specific villager, this could take some time.
The Campsite
After constructing the three homes and after the Resident Services building has been upgraded, Tom Nook will assign you the task of building and placing a campsite on your island.
This campsite will spawn a new villager at random, so be sure to check the campsite every day. By choosing to not talk to the villager in the campsite, they will not move to your island. Instead, a new villager will appear in a few days.
With that said, your very first visitor at the campsite will move to your island. Even if you don't talk to them, you will have to eventually because no other villager will appear at the campsite until you've invited the first one to your island. By talking to the villager twice, you'll have no choice but to invite them to your island, there isn't a "no" option.
How to Remove a Villager From Your Island
Whether you've had enough of their personality or for some other reason, you can encourage a villager on your island to move out.
Encouraging a villager to move out of your island can be very time consuming and it requires a lot of patience.
Choose to Ignore Them
If you decide you really don't like a current villager on your island, don't talk to them. It may be tempting to receive the Nook Miles award for talking to your villagers every day, but by choosing to completely ignore the villager, the chances of them becoming sad and leaving your island will greatly increase.
When ignoring the villager, check in on them every once in a while to see if a cloud appears over their head. When this appears, there's a chance by talking to them that they will ask if they should leave the island. If you encourage them to leave, they will move out.
If you talk to the villager and the option doesn't show to ask them to move out, just give them a few whacks with the bug net.
Report The Villager to Isabelle
Think of Isabelle as the Human Resources department of Animal Crossing: New Horizons. You can change the tune and the flag by talking to Isabelle, but they can also help your cause.
If you complain about the villager enough, you can encourage the villager to move out of your island. You can also force them to change clothes and their catchphrase by reporting them to Isabelle.