To begin:
1. Set the date to 1/01/2021 (New Year's Day), time whatever starting out. If you're just starting the method, 12pm is best in case you get the talk to 3 villagers task for 1000 nook miles.
2. Start the day and check Resident Service's ATM. You automatically get 500 nook miles because of the holiday.
3. After checking the ATM, check your current Nook mile tasks. I only do easy ones like watering flowers, catching snowflakes, hitting rocks, and especially talking to villagers since they gather at Town Hall. I'll also sell fruit if the shop is open.
4. After doing the easy tasks, save and quit the game. On the screen that says "Saving complete, thanks for playing" or something along those lines, minimize the game without closing that prompt and set the time to 4:59am, then quickly hit the home button, go back to your game, close that prompt, and load the game again.
As soon as you walk out of your house, the day should roll over to the 1st again and you unlock new tasks and can check the ATM again!
If you get the task that gives you 1000 Nook miles for talking to villagers at 5am, it is ALWAYS worth it to save and close the game and change the time to 12:00pm on that day.