Disconnect your fan from electrical power.
Use your screwdriver to unscrew the back panel of your fan, and remove any old AC-wiring leading out of the device. Leave an inch or two of exposed wiring leading to the fan's motor. Place a wire nut on the end of the exposed wire to prevent electrical shocks.
Secure your inverter in a location as close as possible to your solar panel. If you are installing a new solar panel for first time use, try to place the panel in a location that has exposure to as much sunlight as possible. Awnings, patios and roof-overhangs are convenient locations as they can provide an additional level of security against poor weather. The inverter is used to convert the DC current provided by the panels into AC current that can be used by your fan.
Run the appropriate wires from the solar panel to the inverter. The solar panel should have two clearly marked wires labeled "Positive" and "Negative." These wires must be connected to the respectively marked DC inputs on the inverter. Depending on the type of inverter you own, you may need to solder the wires in place, though more modern inverters feature a clamping mechanism that makes contact without the need for soldering equipment.
Solder the AC wiring from the inverter to the AC power line leading to the fan motor, be sure to perform the solder away from your wire nut to avoid soldering the nut to the wire. Use electrical tape to cover any exposed wire, then allow your panel to charge up solar energy. Your fan should now be able to run solely from the energy provided by the panel.