Residential solar power systems are what we call “grid tied”. This means that they connect directly to the power grid which is controlled by your local power company. During the day your solar power system will generate too much electricity for you to use, so this electricity is fed back onto the main grid, making your house like a small power station.
At night when the sun is not available to provide your PV panels with sunlight, you simply draw the power you need back off of the grid, or if the grid has failed for some reason you draw the power off of your Sunny Island inverter.
If you want to find out how much power you need to generate then revert back to your old utility bills. If you take a close look at your bill there should be a monthly kWH rating (kilowatt-hour). This is the amount of power you use each month. If at all possible, estimate your average while remembering to account for the change of seasons. You will always use more power in winter.
Remember that the size of your home is completely unrelated to the amount of power you consume.