int x = 1;
Console.WriteLine(x++ + x++);

1. First x++
x is 1
   x++ returns 1
   then x becomes 2

2. Second x++
x is now 2
   x++ returns 2
   then x becomes 3

3. Addition:
   1+2=3

4. Final x:
x = 3

Example to see it clearly:

int x = 1;
int a = x++; // a = 1, x = 2
int b = x++; // b = 2, x = 3
Console.WriteLine(a + b); // 3