Ok, so I grabbed another Nano and got it all wired up like the last one. I soldered a diode directly onto the solenoid valve contacts. Maybe I should have just put it on the circuit board? Anyone think I should? Let me know.
Also, I tried my hand at making a schematic. Let me know if this makes sense.
I'm not plugging anything in until I get at least a little feedback on here. (gulp!)