I thought I might compile a little list, for those reading the thread.
To invite a new villager, you must have an empty plot
put down on your island (not just in your pockets). You then have until 5 AM the next day to invite someone to live in that plot, otherwise someone random will purchase the plot.
A new villager may come from one of the following places:
1. Random
If you place a plot and do nothing, at 5 AM a random villager will move in.
2. Mystery Island
When you have an empty plot available, you will start to see random villagers on the mystery islands again. Talk to them to invite them to live with you. I suggest having enough nook miles to purchase a lot of trips to the islands before setting the plot down, as well as starting with plenty of time. Some people have found dearly wanted villagers on their 20th trip (40,000 miles
).
3. Amiibo cards
I hear that to invite an Amiibo character, you actually have to craft an item for them a total of three times, one item for three days. After giving them the third item on the third day, you can place an empty plot down, talk to them, and you will then be able to invite them into the empty plot. New Horizons is making you work to get that amiibo to move in!
Caution: if you place the plot before the third day, a random will take the plot instead. Only place once third item on third day has been given.
3. Someone else's town
It might be that someone else has a villager that is moving out. The villager cannot only have mentioned moving out, but their belongings must be in boxes (their last day on your friend's island). First, place a plot down on your island, then visit your friend's island and talk to the villager that is in boxes. There will be an option to invite them to live on your island and they will occupy the plot you put down before visiting.
4. Campgrounds
Though I'm unsure if the campgrounds is solely for amiibo, random villagers should show up to the campgrounds as well, at least with how the campgrounds previously worked in ACNL. If you see there's a tent, go inside and see who it is. If you like them, put down a plot and invite them to live on your island. This still needs to be confirmed, I do not know if you would need to craft three items for them as well, but I will edit this post when I find out.
- - - Post Merge - - -
I was just wondering this, I'm going to look into it! I think making a new post will help best, but I'll let you know.