If you're unsure as to when a villager is moving in, set your in-game clock for 5:58am. It'll still technically be the same day that you already loaded up your town. Then quickly save and quit. Wait 2 minutes.
Once you're sure that it's 6am, that means the new day has started, so a villager plot might be out there. So start a new save file and look around for the plot. If you can't find it, and you're 100% sure it isn't there yet, log in to your mayor. Do the same thing; Change the clock to 5:58am (which will again be the same day technically as you loaded up the town), save and quit, wait 2 minutes, then do the same thing with the new character.
It should work the first time, but sometimes it's the second day. I've never had a circumstance where I had to do this 3 times.