Here are the basics. A solar panel charges a battery. When the battery is fully charged, the system turns on a power inverter and switches the appliance from running on grid power to running on the solar power that is stored in the battery. When the battery gets low, the system automatically switches the appliance back to running on grid power. By using the solar power on a duty cycle, you take full advantage of all the available solar power.
I built a simple system that periodically powers a desk lamp for less than $200
For step by step instructions on how to build one of these systems, check out my Instructables page: