How do I size a solar system for my home?

Know how much power you use. The average home in the USA according to the DOE uses 10,299 kWh/year. This is an average rate of 1,174.9 Watts since there are 8766 hours in a year.
Know how much sunlight you receive. The average home in the USA according to the DOE uses its solar panels 18.8% of the time. That means to produce an average of 1,174.9 Watts you will need to have 6,249.4 Watts peak power.
Know what kind of system you want. Do you want to tie to the grid? Or are you in a back woods situation? What is the regulatory environment? These all impact your system. If you use a 100 kWh battery pack and are charging that with solar panels and then discharging the battery into an inverter as you need power, then there will be a 7% loss – so divide by 93% to obtain 6,719.8 Watts peak power. The battery will last half a week without sun.
Have a backup. If you’re totally off-grid consider getting a 3 kW generator to charge your batteries if the sun doesn’t come out for 3.5 days. This means you have to keep it fuelled up, and use it from time to time so it is ready to go if needed. If you’re grid connected you have to pay for the connection and you will pay for power you use during cloudy and dark times, and offset those costs when generating power surplus to your need at sunny times.
Use a qualified solar engineer. Just as you wouldn’t do major surgery without consulting a doctor, or wouldn’t build a house without an architect, you should also not design solar systems without consulting a qualified solar engineer.
A tiny home can get by with a 3.5 kW solar and a 1.5 kW backup generator and a 50 kWh battery pack to run off grid.

A typical home will need 7.0 kW solar and a 3.0 kW backup generator and a 100 kWh battery pack to run off grid.

A luxury home with two electric cars will need 15.0 kW solar and 6.0 kW backup generator and 200 kWh battery pack to run off grid.

In sunnier regions you can reduce the size of your panel and battery pack. In less sunny regions you must increase the size of your panel and battery pack.