Solution 1:

You can query initial array with a help of Linq:

using System.Linq;

...
int[] array = ...

int[] positive = array.Where(item => item > 0).ToArray();

To show positive array in one go you can try string.Join:

Console.WriteLine(string.Join(", ", positive));

You can solve the problem with a help of loops (no Linq solution):

int[] array = ...

int positiveCounter = 0;

foreach (int item in array)
  if (item > 0)
    positiveCounter += 1;

int[] positive = new int[positiveCounter];

int index = 0;

for (int i = 0; i < array.Length; ++i)
  if (array[i] > 0)
    positive[index++] = array[i];

please note, that Array.Copy copies consequent items which is not guaranteed.