First, you must find the gallons per minute (GPM) of the shower head. (You can request a "flow bag" from your local water agency/supplier) Follow the directions on the bag to measure the gallons per minute. . Most showers range from 2-4gpm. If you know your flow or gpm, then you can simply find how many gallons are used in a 10 minute shower. GPM x minutes. This would be a GREAT exercise for an elementary student since the math is relavent.
For those of you who do not wish to measure your shower's gpm, the National Standard in the US is 2.5 gpm, and nearly every shower head available in stores complies with it (though some with a lower flow rate are available).