If you are looking to kick out a villager in Animal Crossing: New Horizons, it's tricky but entirely possible by doing a few select things in the game.
How to kick out villagers in Animal Crossing: New Horizons
There is currently no option to kick villagers out in Animal Crossing: New Horizons, you will instead need to wait until they move off your island. This is random, but all villagers have a small chance to move. You can also try speeding this process up by skipping time or by avoiding the villager you want to kick out.
When they are ready to move out, you will see a cloud over their head. If you see this, walk up and interact with them, and they will tell you they have been thinking about moving off your island. After this, you will be given a choice and if you select yes, the villager will move off your island.
How to kick out villagers using Amiibo cards
Besides merely waiting or avoiding, you can also use Amiibo cards to replace and kick out villagers on your island; but the downside is that you need to pay for these cards. Nonetheless, if you have a card, you can go to Residental Services and replace a villager on your island by selecting the Amiibo option.
However, to replace a villager, you will first need to make sure your island is full because if it is not, the Amiibo villager will simply show up as a camper. That said, when your island is full, you will get a prompt asking you to replace one of your villagers with the Amiibo one, and after this, you should get a list of all villagers on your island. You can then use this list to pick and replace the villager you want to kick out on your island.