How to power solenoid valve?
If the solenoid says 12 VDC on the label, then you can operate it with a 12 V battery. As the solenoid is terminated in two wires, you can just touch the wires to the battery terminals. This assumes the battery is beefy enough to provide all the current that the solenoid tried to draw.
Caution, if you hold one wire in each hand as you disconnect the battery, you may feel a shock. This is due to the inductance of the solenoid producing a high voltage as the current decays quickly on disconnection.
Most people would want something a little more tidy than just connecting wires to the battery. At a minimum, most would chose to use a switch in series.



simulate this circuit &ndash; Schematic created using CircuitLab
If you want to control the solenoid from something, then a relay or transistor will often be used in series as a switch.
Remember that shock you might have got when disconnecting the solenoid. Whatever switches the solenoid, whether it's a switch, relay or transistor, will also get that high voltage on switching off. If it's a high enough rated switch or relay, the metal contacts will not suffer damage, but a weedy relay or transistor needs to be protected by a diode. This is where some of the complications that you refer to come in.