What's the Right Way to use the rand() Function in C++?

Option 2 isn't difficult, here you go:

srand(time(NULL));

you'll need to include stdlib.h for srand() and time.h for time().

srand() should only be used once:

int randint()
{
    int random = rand();
    return random;
}

int main()
{
    // To get a unique sequence the random number generator should only be
    // seeded once during the life of the application.
    // As long as you don't try and start the application mulitple times a second
    // you can use time() to get a ever changing seed point that only repeats every
    // 60 or so years (assuming 32 bit clock).
    srand(time(NULL));
    // Comment the above line out if you need to debug with deterministic behavior.

    char input = 0;
    cout << "Press any character and enter to generate a random number." << endl;

    while (cin >> input)
    {
        cout << randint() << endl;
    }
    keep_window_open();
}

It is common to seed the random number generator with the current time. Try:

srand(time(NULL));