Simple timer to control liquid flow

A 555 in a one shot configuration will likely work just fine for producing the timing. I'm certain you can quickly find on the web a cookbook schematic with those underlined words in the search. The tricky part though maybe the electromagnetic valve you will need to actually control the water. You'll have to identify what kind of water pressure and pipe size will be needed to control. Likely you can get a suitable valve from a place that carries lawn sprinkler parts (Home Depot?) This or your power supply will likely be your major hardware expense. Depending on the water pressure you have to turn off, you might find that the current draw or voltage of the solenoid exceeds the direct capability of a 555 timer circuit. To answer this you can either use a relay (mechanical or solid-state) or a suitable transistor circuit to turn the solenoid on. Oh don't forget to add a reverse biased diode across any coil (relay or solenoid).

Ahh! There's my issue. I have a 12V solenoid to control the water. That's easy. My issue is the pressure change of the incoming water will dictate the end volume. But for now I'd like a simple circuit that I can adjust to up to about 10 seconds (in .1 increments). The 555 is a cool way to go but I've never built anything other than on/off circuits and wig wag headlight controllers.

Now we're getting to the devilish details.

You've recognized that by consistently controlling the time that the valve is open you may not be able to control the actual parameter needed, the volume of water dispensed. The only way that this then can be accomplished consistently is to instead monitor the volume of water dispensed. My suggestion is to still use a 555 timer but only as a fail safe timer circuit. I would instead consider a set reset latching circuit is what directly controls the solenoid. Once the latch starts the water flowing there should be three ways to stop the flow. A manual stop flow button, the 555 timer finishing it's safety time out, and something that measures the water delivered to in effect say enough. Now with a big budget, this could be done with a host of precise measuring instruments. For your scenario I recommend some container that tips itself (like the drinking bird) when full and empties the whole container. In the process of tipping the container moves past an optical switch that resets the latch thus stopping the water flow.