Testing a solenoid is pretty easy but does often take a bit of thought and the correct meter.
Sounds like it may be something you are not familiar with so maybe some explanation first? Sorry if I'm telling you things you already know but there are apt to be others who may not, so here is the short course!
There are water and gas solenoids on our RV and they both work the same in that they are just valves (gates?) that are operated by electrical coils to move the valves.
Since most of our stuff is 12 VDC, we most often find that sort but on things like home dishwashers or washing machines, we are more likely to find they use other voltages, so we need to look at each solenoid to find what voltage it needs to operate.
Basic idea is that when the controls send that voltage through a coil of wire, it makes an electromagnet move the valve inside!
First we need to know the controls are sending power to the solenoid so it can work, so test that.
So to test, we can first check the power going to the coil and that is often not too hard as we find something setting in the water line going to the frig and it will often have two wires, one for in and one for the power coming out.
One test is to measure the voltage going in and at the point where it comes out. If we find voltage going in on one side, we want it to go through the coil and come out the other wire! If power goes in but doesn't come out, the coil wire is broken or "open" and no good!
But another way to test the coil is to measure for resistance from one connection to the other with the wiring off those points. An ohmmeter to measure resistance is what we need there. For this, we don't need to get too techie on how much resistance we expect because if it is going in and through the coil, it is probably okay. Continuity is what we want.
About all the testing we need is to say the coil wire is good all the way through the coil, so whichever method suits best?
But if we find power is getting to the solenoid coil and coming out, so that the coil is good, the next thing that can happen is the thing inside is stuck and not moving. If you put power on and off the solenoid, we can often hear or feel it click or jump as it moves!
There are lots of different solenoids but the idea is they often look something like this.
This is one Norcold solenoid with water in and out and the wire lugs.