Is that all you want to do? What happens after 10 minutes? Does the relay turn back on?
Such code could be as simple as:
const uint8_t pinRelay = 2;
void setup()
{
pinMode( pinRelay, OUTPUT );
}//setup
void loop()
{
digitalWrite( pinRelay, HIGH ); //turn the relay on
delay(10000ul); //wait 10-seconds
digitalWrite( pinRelay, LOW ); //turn the relay off
delay(600000ul); //wait 10 minutes (10 min x 60-sec/min x 1000mS/sec)
}//loop
If you want to do more tasks in between switching the relay on and off you'll need to use, say, the
millis() function to allow you to not use blocking functions like delay().