In order to get more villagers using Amiibo and Amiibo cards you’ll need to unlock the Campground.
The Campground is an area you can create that will allow you to receive visiting villagers on your island, where you can then begin to convince them to stay and live in your town – or you can simply talk and trade with them.
To build the Campground, you must have first upgraded the Resident Services Tent into a proper building (aka the Town Hall). Once completed, Tom Nook will have an assignment to increase your town’s popularity to catch a certain someone’s attention. The first step towards this, will be building a Campground.
You will need to build the Campground Construction Kit, which requires 15 of each type of wood, as well as 15 Iron Nuggets, and then place the kit down in an area you’d like to designate as a campground.
The next day, a random villager will likely appear in the Campground (though you may be able to convince a villager found on a mystery island to be the first to visit the Campground). Whichever villager, you will have no choice but to invite them into your town. After that, villagers may appear at the Campground at any time, but can also be summoned using Amiibo Cards at the Resident Services Terminal.
How to Convince Amiibo Villagers to Move to Your Island
Head to Resident Services and interact with the Nook Stop terminal and select the Amiibo option. Tap your Amiibo or Amiibo Card on the NFC touchpoint (the joystick on the right joycon or the middle of the pro controller, as shown on screen).
It will recognize what Amiibo it is and, if it’s in the game it will work!
When you summon a potential Villager to the Campground, you need to convince them to join your town by making DIY items for them, and it may take several attempts (max 3), requiring you to summon them back each day and craft them an item of their choice until they think about moving in and agree.
This often results in learning new DIY recipes! (But not always.
If you’re dead set on getting an Amiibo Villager to your town do not lay down more land until they’re ready to move in, otherwise a random may snag the spot!
Once they’re down to move to your island, they’ll tell you there’s no space (if you’ve yet to reserve land). No worries though! Just go to Resident Services and ask Tom Nook to sell more land. Return to the villager and tell them to check again and they’ll happily accept the new opening. The villager will agree to move in and appear a day or 2 later.