Java Adding 2 arrays together and return the sum of it

First, you need to instantiate the array correctly:

int[] sumArray = new int[ar1.length];

Then, if you want to see what is the result, you need to do something with it (print it maybe...):

System.out.println( Arrays.toString( sumA(ar1, ar2)) );

If you want to add arrays with different lengths:

private static int[] sumA(int[] ar1, int[] ar2) {
    int[] sumArray = new int[Math.max(ar1.length, ar2.length)];

    for (int i = 0; i < sumArray.length; i++) {
        sumArray[i] = (i < ar1.length ? ar1[i] : 0) + (i < ar2.length ? ar2[i] : 0);
    }
    return sumArray;
}

If not, BobTheBuilder's answer is sufficient.

Your error is here:

int[] sumArray = new int[0]; <---

you need to instantiate the array with the length of one of the two parameters.

Try this:

int[] sumArray = new int[ar1.length];

or this

int[] sumArray = new int[ar2.length];

and if you want to show results:

int[] sumArray = new int[ar1.length];

for (int i = 0; i < ar1.length; i++)
{
    sumArray[i] = ar1[i] + ar2[i];
    System.out.print(sumArray[i] + " ");
}
return sumArray;

That's because you are not writing any system.out.println(); statements in your code. Try this code:

public class MyProgram
{
public static void main (String[] args)
{
    new MyProgram().start();
}

public void start()
{
    int[] ar1 = {3, 8, 4, 9, 5, 5, 23, 14};
    int[] ar2 = {33, 23, 41, 9, 17, 51, 23, 45};

    int sum[]=sumA(ar1, ar2);

    for(int i: sum)
    {
        System.out.println(i);
    }
}

private int[] sumA(int[] ar1, int[] ar2)
{
    int[] sumArray = new int[8];

    for (int i = 0; i < ar1.length; i++)
    {
        sumArray[i] = ar1[i] + ar2[i];
    }
    return sumArray;
}
}

See the image attached.