Would this be the same as how a smoke alarm works. When the 9v battery gets low and requires replacing it sets off an audible chirp and a red led light flashes?
Yes, except in your case it would fire up the transmitter and send a pulse to the receiver indicating "low battery" at pre-determined time intervals. Or you could mount a water-proof button on the transmitter case that would cause the μP to test the battery and light up an LED if the battery was okay. No transmitter necessary for that, but the automatic transmit to the receiver when the battery gets low could be more convenient. The receiver may require another microprocessor to decipher the four digital signals (three float switches and low-battery) and act accordingly. Or you may choose to send valve-control signals to the receiver (instead of float switch states) and connect those to relays controlling the two valves. No μP at the receiver needed for that. You have to decide how many and what kind of "bells and whistles" to add.
It looks like the transmitter/receiver pair you bought could work "as is" for valve control without the battery-saving microprocessor feature, but then I really cannot recommend a suitable battery because I don't know how often it would transmit, or even how you would arrange for the transmitter to "fire up" momentarily and transmit on switch change. I suppose this could be done with discrete CMOS logic at acceptably low energy consumption, but a CMOS μP (like the PIC10F206 I am currently playing with) would seem to be a less complicated path. I think if I were you I would do some investigation to see what kind of PIC (or other μP) would be most suitable. In other words, define what you want it to do, determine how many input ports (bits) you need to look at, decide whether an analog-to-digital converter or analog comparator (for measuring battery voltage under load) is necessary, determine how many output ports (bits) you need to send three, four, or five signals to the transmitter (including a "battery-low" signal), activate a "dummy load" for battery test, and activate the transmitter.
I haven't thought this completely through, but it appears that each valve will be driven clockwise or anit-clockwise (two control lines) until a micro-switch limit is reached. Each valve needs a 24 V AC supply to energize its motor, so two relays for each valve are required: one to select direction, one to turn on the motor. Or you can wire the relays so each one selects one direction and turns on the motor. Since there are two valves, you need four control line signals coming from the transmitter to the receiver, plus maybe a fifth line for low-battery notification. All the valve-control logic, based on the states of the three float switches, would take place at the transmitter. You could add some water-proof switches there to control the mode of operation: drain the pool, fill the pool, perhaps over-ride the float switches, but you can do the same thing at the valve actuators by simply flipping the three-position toggle switch on the actuator to the appropriate position. Just remember to restore it to the "center off" position to allow automatic operation from the receiver.
We used to have a fellow here who was quite good at taking a set of performance specifications and designing a circuit, complete with parts list and bill of materials and schematic wiring diagram, usually overnight. Unfortunately Kris died earlier this year and no one has stepped up to fill his shoes. I am sure that collectively we have the talent, but not everyone has the time available to do what Kris did. I and others here will help you learn how to use microprocessors, and we even have a forum here dedicated just for that, but you must do most of the work yourself. We will provide guidance as needed.
Hop