This probably isn't the most elegant way but it works :D I've returned the value but printed also it within the function.

1. 
   
   void setup(){
    noLoop();
   }
   void draw(){
    
    int[] myArray = new int[10];
    for(int i=0; i<10; i++){
     myArray[i]=int(random(10));
    }
    
    get_second_max(myArray);
2. 
   }
   
   int get_second_max(int myArray[]){
    
     int iMax=0;
     int iMax2=0;
   
    
     for(int i=0;i<10;i++){
     
       if(myArray[i] >= iMax) iMax = myArray[i];
       if((myArray[i] >= iMax2) && (myArray[i]!=iMax)) iMax2 =myArray[i];
       println(myArray[i]);
     }
    
     println("Biggest = " + iMax);
     println("Second Biggest = " + iMax2);
    
     return(iMax2);
    
   }
   

I would have made similar code, but changing the loop to:
  for (int i = 0; i < myArray.length; i++) {
to work with any array.

A little refinement would avoid checking for iMax2 if >= iMax.

A better code:

1. void setup()
2. {
3.   get_second_max(new int[] { 1 });
4.   get_second_max(new int[] { 1, 2 });
5.   get_second_max(new int[] { 1, 2, 3 });
6.   get_second_max(new int[] { 1, 2, 3, 5 });
7.   get_second_max(new int[] { 1, 2, 3, 5, 7 });
8.   get_second_max(new int[] { -1, 2, -3, 5, -7 });
9.   get_second_max(new int[] { 1, 2, 3, 5, 7, 5, 3, 2, 1 });
10.   exit();
    
11. }
12. int get_second_max(int[] array)
13. {
14.   int max1 = Integer.MIN_VALUE;
15.   int max2 = Integer.MIN_VALUE;
16.  
17.   for (int i = 0; i < array.length; i++)
18.   {
19.     if (array[i] > max1)
20.     {
21.       max2 = max1;
22.       max1 = array[i];
23.     }
24.     else if (array[i] > max2)
25.     {
26.       max2 = array[i];
27.     }
28.   }
29.  
30.   println("Biggest = " + max1);
31.   println("Second Biggest = " + max2);
32.  
33.   return max2;
34. }