How can this Java code be optimized?

What I'd made and make sense for me, hope it'll help you:
You named it Lotto, and unless the rules changed, we can't replay when we've lost, so the loop while(true) is useless in your code ;)

public class Lotto {

    private static final int INPUT_SIZE = 6;

    private static final int MIN_NUMBER_POSSIBLE = 0;

    private static final int MAX_NUMBER_POSSIBLE = 25;

    private Set<Integer> userNumbers = new HashSet<Integer>();

    private Set<Integer> randomNumbers = new HashSet<Integer>();

    public static void main(String[] args) {
        Lotto c = new Lotto();
        c.generateRandomNumbers();
        System.out.println("Pick " + INPUT_SIZE + " numbers from " +  MIN_NUMBER_POSSIBLE +  " to " + MAX_NUMBER_POSSIBLE + ".");
        c.readUserNumbers();
        if (c.doUserNumbersMatchRandomNumbers()) {
            System.out.println("You win :) !");
        } else {
            System.out.println("Sorry you failed :( !");
            c.showRandomNumbersToUser();
        }
    }

    private void generateRandomNumbers() {
        Random random = new Random();
        for (int i = 0; i < INPUT_SIZE; i++) {
            randomNumbers.add(random.nextInt(MAX_NUMBER_POSSIBLE));
        }
    }

    private void showRandomNumbersToUser() {
        System.out.println("\nRandom numbers where : ");
        for (Integer randomNumber : randomNumbers) {
            System.out.println(randomNumber + "\t");
        }
    }

    private void readUserNumbers() {
        Scanner input = new Scanner(System.in);
        int inputSize = 1;
        while (input.hasNextInt() && inputSize < INPUT_SIZE) {
            int numberChoosen = input.nextInt();
            if (numberChoosen < MIN_NUMBER_POSSIBLE || numberChoosen > MAX_NUMBER_POSSIBLE) {
                System.out.println("Your number must be in " + MIN_NUMBER_POSSIBLE + " - " + MAX_NUMBER_POSSIBLE + " range.");
            } else {
                userNumbers.add(numberChoosen);
                inputSize++;
            }
        }
    }

    private boolean doUserNumbersMatchRandomNumbers() {
        for (Integer userNumber : userNumbers) {
            if (!randomNumbers.contains(userNumber)) {
                return false;
            }
            printMatchingNumber(userNumber);
        }
        return true;
    }

    private void printMatchingNumber(int num) {
        System.out.println("Your number, " + num + ", has been called.");
    }
}

First, you need just one Scanner.

Second, you could store the number choose by the user in an array.

Third, you could iterate the array to find the number there, instead of doing a lot of if and else if.

Forth, the user always wins. This looks like a bug. The while(true) ensures that the numbers are choosen in a way that eventually all the choosen numbers will be drawn. More, nothing stops the user from choosing a number more than once.

Fifth, the wait(100) will fail. You should use Thread.sleep(100) instead. EDIT, oops, I thought you were using Object.wait. It currently works, but Thread.sleep is better.

One small thing I noticed is the call to rand.nextInt(25). The player is told to select a number between 1 and 25, but rand.nextInt(25) will only generate 0 - 24. Change it to one of the following:

• rand.nextInt(25) + 1
• rand.nextInt(26) (if you want to include the 0 =))

What not to do:

Using single numbered variables that have the same function... This works but it becomes tedious as the program gets larger and more complex.

What to do:

-> Favor the use of "arrays" instead.

Arrays are explained here for use in Java: http://docs.oracle.com/javase/tutorial/java/nutsandbolts/arrays.html

I'm no java expert but you could start unitizing things. Your code needs to be less repetitive.

Like this, write functions for what you need to keep doing.

int AcceptInt()
{
    Scanner numSc = new Scanner(System.in);
    return numSc.NextInt();
}

Untested code, I don't even have Java on my PC. But it should give you some direction. Hope I haven't made any silly typos, I used notepad.

public class Lotto {

    //Pick 6 numbers from 1 to 100
    //If all of your numbers gets called out, you win

    public static void wait (int n) throws InterruptedException 
    {
        Thread.sleep(n*1000);//*1000 for seconds?
    }

    static int[] nums = new int[6];
    static boolean[] states = new boolean[6];

    public static void main(String[] args) {
        Random rand = new Random();
        //set all to false.
        //dunno if java defaults boolean to false.
        int i = 0;
        while(i++<6) { states[i] = false; }

        System.out.print("Pick 6 numbers from 0 to 25.");
        for(int k=0; k<6; k++) {
            System.out.print("Gimme number :"+ k);   
            nums[k] = AcceptInt();//check for validity?
            System.out.println();
        }
        System.out.println("Numbers will now start to be drawn, if all of your numbers are called, you win.");

        while (true) {//Shouldn't this be finite?
            int random = rand.nextInt(25);
            System.out.println("Number " + random + ".");

            for(int l= 0;l<6; l++) {
                if (random == nums[l]) {
                    states[l] = true;
                    System.out.println("Your number, " + nums[l]+ ", has been called.");
                }
            }

            for(int j= 0;j<6; j++)
            {
                if(states[j] == false)
                {
                    break;
                }
                System.out.println("You win!!");
                //maybe set another flag here and break out of your 
                //while infinite loop.
            }
            wait(100);//assuming seconds?
        }
    }
    static int AcceptInt()
    {
     Scanner numSc = new Scanner(System.in);
     return numSc.NextInt();
    } 
}

I have modified the code, executed and played too. Good game :)

I have used ArrayList because it has enough built-in methods to handle this scenario easily.

You should also validate if user is entering a number outside of 0 and 25. That's very important. This will force user to enter the nth number only between 0 to 25 otherwise it will not go for next number.

public static void main(String[] args) throws InterruptedException {
    Random rand = new Random();
    Scanner scan = new Scanner(System.in);
    System.out.print("Enter 6 numbers from 0 to 25 separating.\n");
    List<Integer> list = new ArrayList<Integer>();
    for (int i = 0; i < 6; i++) {
        boolean flag = false;
        do {
            System.out.println("Enter " + (i+1) + "th number :");
            int num = scan.nextInt();
            if (num > -1 && num < 26) {
                list.add(new Integer(num));
                flag = false;
            } else {
                System.out.println("not valid number.");
                flag = true;
            }
        } while(flag);
    }
    System.out.println("Numbers will now start to be drawn, you win if all of your numbers are called.");
    for (int i = 0; i < 6; i++) {
        Integer random = new Integer(rand.nextInt(25));
        if (list.contains(random)) {
            System.out.println("Your number, " + random +", has been called.");
            list.remove(random);
        }
        Thread.sleep(1000);
    }
    if (list.size() == 0) {
        System.out.println("You won...");
    } else {
        System.out.println("You didn't win...");
    }
}

OUTPUT:

Enter 6 numbers from 0 to 25 separating.
Enter 1th number :
12
Enter 2th number :
34
not valid number.
Enter 2th number :
54
not valid number.
Enter 2th number :
15
Enter 3th number :
-23
not valid number.
Enter 3th number :
4
Enter 4th number :
5
Enter 5th number :
-100
not valid number.
Enter 5th number :
34
not valid number.
Enter 5th number :
10
Enter 6th number :
9
Numbers will now start to be drawn, you win if all of your numbers are called.
Your number, 9, has been called.
Your number, 4, has been called.
You didn't win...

You can make your numScan and numCor into arrays and use a for loop to access them.