I was looking back at reddit posts (while deleting them), and I realized I’d written a book worth of stuff about this topic. I would write it all again, if it is helpful. But for a brief synopsis of “how it works”, here is what one does:
Assess power needs - look at your living standard and catalog all the devices you power, and estimate the time they operate - power is measured in watts, and time in hours. Multiply to get watt-hours; then divide by 1000 to get kilowatt hours. Compare with your utility bill.
Nowadays, I have a grid connection with a venerable Intermatic timer switch. The switch has adjustable tabs on a 24-hour mechanical clock. When the timer reaches an “ON” tab, the switch energized an 80-amp contactor which connects my inverter to the grid. Once the inverter decides the grid power is stable and in the proper voltage range, it quits using battery power and starts passing grid power to my house service panel. Although the house main disconnect is 100-amp capacity, the inverter is only 4kW, which corresponds to peak amperage of 16 amps at 240 or 32 amps at 120, more or less, so even the 80 amp contactor is a bit of overkill for now - but you never know when I might have to replace the inverter, so 80 amps give some flexibility. Anyway, I have removed the ON tab so the grid power never reaches the house.