Question
Matt,

I know exactly where the valves are (I believe there are 2 green boxes around my yard).  How do I actually clean the valve?

Answer
OK good.
You'll need to dig around them till you have a hole open that is deeper than the valves and pipe. don't be surprised if you find more than one valve in the hole. Also be careful, all of the wires are in the hole. You don't want to cut them in the process.
Before you start, take a digital picture of the valves. It can be a valuable reference to reassembling the valves. To identify the valves, turn on the valve (with the controller)that is giving you the problem. You should feel/hear it buzz a little. Now, shut off the water supply. Unscrew the screws that hole the top on. You may see the contaminant in the valve, remove it. If not turn on the water supply just a little, this should flush the junk out. (it's good the have a little help here to watch the valves) Too much water will just fill the hole and get more dirt in the valves.
Once you feel the dirt/ stones are out reinstall the valve top and turn the water on.
Hopefully, this will resolve the problem.

Matt