This is a simple fix. The water line coming in the back of the refrigerator goes right into the solenoid. After you remove the retaining screws for the small back panel that keeps you form seeing the water valves you can begin to replace it. There should be two valves, one for the ice maker and one for the water dispenser. If they are one unit you have to change them together but if separate you need to select the correct one. If you hit the dispenser handle and can hear the clicking of the valve then it is that one. If you can't then in gage the ice maker, the ice maker valve will hum, you need the other one.
UNPLUG the refrigerator and turn off the water to the frig. Notice where the wires are connected to the solenoid, mark it down on a paper. If it is an exact replacement then you will just unplug the wires and they will re-install the same way. If it is a substitute you may have to use wire nuts or whatever is suggested in the new valves instructions. Next you have to remove the water outlet that goes to the water dispenser. This would be both lines if it is one unit for both ice and water dispensers. Then the two mounting screws on the frame should have it out in your hand. Re-assemble in reverse order.
If you are just replacing the solenoid, the coil that opens the valve then when you have the assembly off in you hand you will see the coil or coils on one side with a retaining plate screwed to the valve assembly, probably 4 1/4 inch hex drive screws holding it in place. Remove these screws and the plate and coil will separate from the valve body. Spring, plastic and rubber that open when the coil is energized will be exposed also, be careful and open slowly. The new coil will go back the same way as the old one. Make sure the gasket is back in the correct place and that the valve is reassembled correctly and replace the screws finger tight. Then using the nut driver tighten a little at a time corner to corner in a X pattern until all screws are tight (don't over tighten and strip the holes). Replace everything in reverse order. You should be back in business.
Be sure that the water valve is the problem and not that you have the water set to cold and the line is freezing, one of the common problems with these.
Hope this was well enough explained, good luck.
I can't find a photo of the GE but here is a Whirlpool fridge..