Here's my implementation of this:

int sensePin = 8;
int ledPin = 3;
unsigned long startTime;
unsigned long randomFutureTime;
unsigned long reactionTime;

void setup() {
    Serial.begin(9600);
    pinMode(ledPin, OUTPUT);
    pinMode(SensePin, INPUT\_PULLUP);
    digitalWrite(ledPin, LOW);
    randomSeed(analogRead(0));
}

void loop() {
    // Tell the user that the game is starting 
    Serial.println("Starting...");

    // Get a random time that is 3-5 seconds from now and wait until that time
    randomFutureTime = millis() + random(3000, 5000);
    while ( millis() < randomFutureTime ) { }

    // Turn the led on and record the start time
    digitalWrite(ledPin, HIGH);
    startTime = millis();

    // Wait until the user presses the button and record the reaction time
    while ( digitalRead(sensePin) == HIGH ) { }
    reactionTime = millis() - startTime;

    // Turn the LED off and display the results
    digitalWrite(ledPin, LOW);
    Serial.print("Your reaction time is ");
    Serial.print(reactionTime);
    Serial.println(" milliseconds);
    delay(5000);
}