Hi Steven,
All you need is a 555 timer IC wired as a monostable like in our Articles section. A momentary pushbutton shorts its pin 2 to ground to start the timing and a resistor and capacitor on pin 6 determine the time period. Connect pin 7 also to pin 6. Its output can drive a relay coil with up to 200mA. Add a diode across the relay coil to arrest its back-EMF spike.