How do you keep shower temperature from changing when someone flushes the toilet or uses another sink?

Your water pressure is low. Consequently, when cold water is diverted to another application such as a toilet or a sink, the amount of cold water available at the shower mixing valve decreases as the low pressure is unable to keep up with the shower's demand. This causes a hotter mixture at the shower head. The solution is to either improve the cold water supply to the shower or to replace the shower control valve with a temperature compensating type. Pressure balancing is the cheapest and simply changes the shower temperature according to the pressure in the cold and hot water lines. When the toilet or sink is used, reduced pressure to the shower valve is detected and the valve reduces the hot water pressure, thereby maintaining the temperature. The more sophisticated approach is a thermostatic shower control valve. These are significantly more expensive, but will not reduce the pressure at the shower head (a drawback of the pressure balancing valve). The thermostatic valve would be required when one shower control valve is operating several shower heads. Moen, Kohler and Delta all make both types of control valves. They can be readily obtained from a local Plumbing supply house.