NOTE: make sure you use earth-friendly cleaning products if you do this! There are a lot of good cleaners that use natural surfactants.
ALSO NOTE: In spite of this image, taken after a week of gardening and summer fun, employing greywater does NOT mean you must live in filth! (This pic was snapped just before I scrubbed with Bon Ami.) (I'm new at this.)
Step 1: Buy a Hand-pump at the Hardware Store.
This is the $9 part. Ask for a hand pump, a suction pump, or a cheap plastic pump for about $5 at your local hardware store. Also purchase a few yards of hose that will fit on the end of the accordion-folded hose that comes attached to the pump.
Step 2: Close the Drain When You Take a Shower.
The first person in the shower each morning closes the drain, and we collect water from up to three showers, which can fill up the bathtub halfway (about 40 gallons, I think). The last person starts the pump, which we keep on a hook inside the shower window when not in use.
It typically takes 5-10 quick squeezes to get the pump flowing. You can adjust the suction with the little nozzle on top of the pump.
Used shower water is usually not very hot. I usually let a bath cool before emptying it with the pump, however.
Step 3: The Water Goes Out the Window.
Insert the vinyl tube into the male end of a garden hose that's long enough to take the water where you want it. (Garden hose not included in the $9 budget.)
Step 4: Secure the System Outside.
The vinyl tube stays in the window all summer, and can be brought inside after the season ends so you can close your window in winter.
The hoses get a little grungy on the inside over a year or two -- but it costs almost nothing to replace the whole system!
The first year we used this we cut our water bill in half!