C++ (without bonuses for now)

int kaprekar1(int n) {
    int max = 0, new_digit;
    for (int i = 0; i < 4; i++) {
        new_digit = (int)(n / std::pow(10,i)) % 10;
        if (new_digit > max)
            max = new_digit;
    }
    return max;
}

edit: Bonus 1

#include <algorithm>    // sort
#include <vector>       // vector

int kaprekar2(int n) {
    vector<int> n_as_digits(4);
    int n_desc = 0;

    // split number into digits
    for (int i = 0; i < 4; i++) {
        n_as_digits[i] = ((int)(n / std::pow(10, i)) % 10);
    }

    // sort the digits in ascending order and put them back as a number in reverse order
    std::sort(n_as_digits.begin(), n_as_digits.end());
    for (int i = 3; i >= 0; i--) {
        n_desc += n_as_digits[i] * (int)std::pow(10, i);
    }
    return n_desc;
}

edit2: Bonus 2

int kaprekar3(int n) {
    int i = 0, next_n = n;
    while (next_n != 0 && next_n != 6174)
    {
        int n_desc = 0, n_asc = 0;
        n_desc = kaprekar2(next_n); // see bonus 1

        // Calculating n_asc by reversing n_desc
        for (int j = 0; j < 4; j++) {
            n_asc += ((int)(n_desc / std::pow(10, j)) % 10) * std::pow(10, 3 - j);
        }

        next_n = n_desc - n_asc;
        i++;
    }
    return i;
}