There are many ways to do this, but yes, it involves generating a random int (using e.g. java.util.Random.nextInt) and then using that to map to a char. If you have a specific alphabet, then something like this is nifty:

    import java.util.Random;

    //...

    Random r = new Random();

    String alphabet = "123xyz";
    for (int i = 0; i < 50; i++) {
        System.out.println(alphabet.charAt(r.nextInt(alphabet.length())));
    } // prints 50 random characters from alphabet

Do note that java.util.Random is actually a pseudo-random number generator based on the rather weak linear congruence formula. You mentioned the need for cryptography; you may want to investigate the use of a much stronger cryptographically secure pseudorandom number generator in that case (e.g. java.security.SecureRandom).