In Java 1.7 or later, the standard way to do this is as follows:

import java.util.concurrent.ThreadLocalRandom;

// nextInt is normally exclusive of the top value,
// so add 1 to make it inclusive
int randomNum = ThreadLocalRandom.current().nextInt(min, max + 1);

See the relevant JavaDoc. This approach has the advantage of not needing to explicitly initialize a java.util.Random instance, which can be a source of confusion and error if used inappropriately.

However, conversely there is no way to explicitly set the seed so it can be difficult to reproduce results in situations where that is useful such as testing or saving game states or similar. In those situations, the pre-Java 1.7 technique shown below can be used.

Before Java 1.7, the standard way to do this is as follows:

import java.util.Random;

/**
 * Returns a pseudo-random number between min and max, inclusive.
 * The difference between min and max can be at most
 * <code>Integer.MAX_VALUE - 1</code>.
 *
 * @param min Minimum value
 * @param max Maximum value.  Must be greater than min.
 * @return Integer between min and max, inclusive.
 * @see java.util.Random#nextInt(int)
 */
public static int randInt(int min, int max) {

    // NOTE: This will (intentionally) not run as written so that folks
    // copy-pasting have to think about how to initialize their
    // Random instance.  Initialization of the Random instance is outside
    // the main scope of the question, but some decent options are to have
    // a field that is initialized once and then re-used as needed or to
    // use ThreadLocalRandom (if using at least Java 1.7).
    // 
    // In particular, do NOT do 'Random rand = new Random()' here or you
    // will get not very good / not very random results.
    Random rand;

    // nextInt is normally exclusive of the top value,
    // so add 1 to make it inclusive
    int randomNum = rand.nextInt((max - min) + 1) + min;

    return randomNum;
}

See the relevant JavaDoc. In practice, the java.util.Random class is often preferable to java.lang.Math.random().

In particular, there is no need to reinvent the random integer generation wheel when there is a straightforward API within the standard library to accomplish the task.

For iterating backwards see this answer.

Iterating forwards is almost identical. Just change the iterators / swap decrement by increment. You should prefer iterators. Some people tell you to use std::size_t as the index variable type. However, that is not portable. Always use the size_type typedef of the container (While you could get away with only a conversion in the forward iterating case, it could actually go wrong all the way in the backward iterating case when using std::size_t, in case std::size_t is wider than what is the typedef of size_type):

Using std::vector

Using iterators

for(std::vector<T>::iterator it = v.begin(); it != v.end(); ++it) {
    /* std::cout << *it; ... */
}

Important is, always use the prefix increment form for iterators whose definitions you don't know. That will ensure your code runs as generic as possible.

Using Range C++11

for(auto const& value: a) {
     /* std::cout << value; ... */

Using indices

for(std::vector<int>::size_type i = 0; i != v.size(); i++) {
    /* std::cout << v[i]; ... */
}

Using arrays

Using iterators

for(element_type* it = a; it != (a + (sizeof a / sizeof *a)); it++) {
    /* std::cout << *it; ... */
}

Using Range C++11

for(auto const& value: a) {
     /* std::cout << value; ... */

Using indices

for(std::size_t i = 0; i != (sizeof a / sizeof *a); i++) {
    /* std::cout << a[i]; ... */
}

Read in the backward iterating answer what problem the sizeof approach can yield to, though.