I want to control two solenoid valves with a single Arduino and allow them to operate at the same time with a total voltage no greater than 12V. How should I go about doing this?
You could use a relay module such as the 2 channel model linked below. These modules are available in 1, 2, and 4 channel versions.
If you need assistance hooking it up and programming it, check out this tutorial. (The first one I came across, but seems good.)
For driving DC loads like a solenoid valve I would highly recommend using a MOSFET. Relays are great for switching AC and DC loads especially when current is very high but they’re not required for this application. They also take a lot of current to switch relative to a MOSFET. MOSFET are also used to switch to coil on large relays which is a solenoid in the relay.
Sparkfun have an article on them here:
Here’s an article the Core-Electronics site points to: