How does the static modifier affect this code?

In Java two phases take place: 1. Identification, 2. Execution

1. In identification phase all static variables are detected and initialized with default values.

   So now the values are:
   A obj=null
num1=0
num2=0

2. The second phase, execution, starts from top to bottom. In Java, the execution starts from the first static members.
   Here your first static variable is static A obj = new A();, so first it will create the object of that variable and call the constructor, hence the value of num1 and num2 becomes 1.
   And then, again, static int num2=0; will be executed, which makes num2 = 0;.

Now, suppose your constructor is like this:

 private A(){
    num1++;
    num2++;
    System.out.println(obj.toString());
 }

This will throw a NullPointerException as obj still has not got a reference of class A.